Optimal Portfolios with One Risky Security

This second edition provides a rigorous yet accessible graduate-level introduction to financial economics. Since students often find the link between financial economics and equilibrium theory hard to grasp, less attention is given to purely financial topics, such as valuation of derivatives, and more emphasis is placed on making the connection with equilibrium theory explicit and clear. This book also provides a detailed study of two-date models because almost all of the key ideas in financial economics can be developed in the two-date setting. Substantial discussions and examples are included to make the ideas readily understandable. Several chapters in this new edition have been reordered and revised to deal with portfolio restrictions sequentially and more clearly, and an extended discussion on portfolio choice and optimal allocation of risk is available. The most important additions are new chapters on infinite-time security markets, exploring, among other topics, the possibility of price bubbles.

This second edition provides a rigorous yet accessible graduate-level introduction to financial economics. Since students often find the link between financial economics and equilibrium theory hard to grasp, less attention is given to purely financial topics, such as valuation of derivatives, and more emphasis is placed on making the connection with equilibrium theory explicit and clear. This book also provides a detailed study of two-date models because almost all of the key ideas in financial economics can be developed in the two-date setting. Substantial discussions and examples are included to make the ideas readily understandable. Several chapters in this new edition have been reordered and revised to deal with portfolio restrictions sequentially and more clearly, and an extended discussion on portfolio choice and optimal allocation of risk is available. The most important additions are new chapters on infinite-time security markets, exploring, among other topics, the possibility of price bubbles.

This thesis consists of three essays in financial economics, more precisely in the field of asset pricing and optimal portfolio choice. The first essay studies the asset pricing implications of heterogeneity in preferences coupled with long run risk in a dynamic general equilibrium pure exchange economy. It is concerned with the understanding of how risk sharing among different types of agents affects the assets returns moments in equilibrium and moreover, how these agents reacts dynamically to the long run risk that they perceive. The second and third essay approach the question of optimal portfolio with stochastic opportunity sets. The second essay proposes an approximation methodology for deriving approximate closed form solutions of dynamic optimal portfolio allocation problems. The third essay examines the optimal consumption, portfolio rule and life insurance purchase problem of a wage earner having uncertain lifetime when the market price of risk follows a mean-reverting stochastic process.

This article extends the optimal covariance steering (CS) problem for linear stochastic systems subject to chance constraints so as to account for an optimal allocation of the risk. Previous works have assumed a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">uniform</i> risk allocation in order to cast the optimal control problem as a semidefinite program, which can be solved efficiently using standard SDP solvers. An iterative risk allocation (IRA) formalism is used to solve the optimal risk allocation problem for CS using a two-stage approach. The upper-stage of IRA optimizes the risk, which is a convex problem, while the lower-stage optimizes the controller with the new constraints. The process is applied iteratively until the optimal risk allocation that achieves the lowest total cost is obtained. The proposed framework results in solutions that tend to maximize the terminal covariance, while still satisfying the chance constraints, thus leading to less conservative solutions than previous methodologies. In this article, we consider both polyhedral and cone state chance constraints. Finally, we demonstrate the approach to a spacecraft rendezvous problem and compare the results with other competing approaches.

The proliferation of novel preference theories in financial economics is hampered by a lack of non-experimental evidence and by the theories’ additional complexity which has not been shown to be critical in applications. In this article I present arguments in support of preferences with rank dependency. Using the Survey of Consumer Finances data, I document two widespread patterns inconsistent with expected utility: (i) many households simultaneously invest in well-deversified funds and in poorly-diversified portfolios of stocks; and (ii) some households with substantial savings do not invest anything in equities. I show that portfolio choice models with rank-dependent preferences, plausibly parameterized and under fully rational assumptions, are quantitatively consistent with the observed diversification. These results call for further efforts to integrate the models of rank-dependent preferences in portfolio theory and asset pricing. The decision theoretic literature has long acknowledged the shortcomings of the expected utility theory of Von Neumann and Morgenstern (1944). Several generalizations of the theory are inspired by the experimental evidence and aimed at improving its descriptive accuracy. However, there are few applications of new models of preferences in finance, and expected utility continues to dominate the field. 1 Two principal hurdles slow the proliferation of novel preferences in financial economics: first, the lack of empirical (non-experimental or ‘‘field’’) data confirming that the behavior motivating non-expected utilities is widespread outside the laboratory settings; second, the additional and often significant complexity of the alternative preferences which has not been shown to be critical in applications where the models based on expected utility fall short of reasonable predictions. This article presents empirical and theoretical This paper was previously circulated under the title ‘‘Household Portfolio Diversification.’’ The paper has benefited from the comments of Shlomo Benartzi, Luca Benzoni, Markus Brunnermeier, John Dickhaut, Maria Perozek, Raj Singh, Hersh Shefrin, and workshop participants at Minnesota Finance bag lunch, 2003 Wharton conference ‘‘Household Financial Decision Making and Portfolio Choice’’ and 2003 summer meetings of Econometric Society. I would like to thank Cam Harvey (the editor) and an anonymous referee for many helpful comments and suggestions. A special thanks to Jack Kareken for comments and editorial help on an earlier draft. I am grateful to Donna Zerwitz for editorial assistance. The views expressed herein are those of the author and not necessarily of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. All errors and omissions are the sole responsibility of the author. Address correspondence to Valery Polkovnichenko, Finance 3-122 CSOM, 319 19 th

Reviewed by: Circles of Compensation: Economic Growth and the Globalization of Japan by Kent E. Calder Frances McCall Rosenbluth Circles of Compensation: Economic Growth and the Globalization of Japan. By Kent E. Calder. Stanford University Press, 2017. 320 pages. Hardcover, $90.00; softcover, $29.95. A new book by Kent Calder is always cause for cheer, and this one is no exception. Circles of Compensation puts Calder's scholarly gifts on full display: it advances a broad argument, relates the argument to relevant social science theories, anchors it historically, illustrates it with careful attention to detail across a wide range of issue domains, and, finally, proposes possible policy solutions. Japan, says Calder, has had a tendency to promulgate policies that favor insiders—or, in other words, create circles of compensation. These policies internalize benefits and externalize costs, shifting them onto others, most notably consumers and taxpayers. The banking system favors banks over savers; land policy favors the construction industry and developers over residents; food policy favors farmers over consumers; energy policy favors the energy industry over general citizens; transportation policy favors the transportation industry over users; and the media market favors media producers over the general public and foreign journalists. Why does Japan operate this way? Why are these arrangements both widespread and stable, and how is it that they have survived Japan's integration into the world economy? Calder recounts familiar explanations for Japan's persistent "iron triangle" of politicians, bureaucrats, and business insiders: late-developer "catch-up" industrialization, a strong bureaucratic apparatus capable of enforcing insider deals, a relatively homogeneous population, and politicians eager to raise campaign contributions from the benefiting industries for expensive election campaigns. Calder's emphasis is on the strength of intermediate associations of insiders that form the circles of compensation capable of defending their advantages in the face of successive would-be newcomers. Protective regulations, however they might discourage innovation or affect the Japanese economy as a whole, allow insiders to insure themselves against failure; these insiders are then able to foist the requisite "insurance premiums," so to speak, onto outsiders, most notably the general population. Calder offers by contrast the auto industry, which was never as well cartelized as many other Japanese industries, as an example of successful innovation and globalization. Circles of Compensation is far richer than this review can fully capture: the book overflows with fascinating details, interpretations, and implications. In the chapters on finance and on land and housing (chapters 4 and 5, respectively), Calder explains how during Japan's period of postwar economic expansion an attachment to real estate as the principal form of collateral favored the construction industry and real estate developers. But Japan's economy is no longer a closed system, and new laws in the 1980s allowing capital outflows (and, by extension, offering alternatives to domestic savings) pulled the rug out from under land prices in Japan. The government's [End Page 146] response, to prop up the stability of banking and real estate with easy money rather than to change collateral rules, set the stage for the asset bubble that reached vertiginous heights before bursting in 1991. Thus ended the glory days of postwar Japan. The bursting of the asset bubble also ended the illusion that Japan had invented a superior form of capitalism with an optimal allocation of risk and reward. The system that had been built on circles of compensation was not, as some had hoped, a kinder, gentler capitalism favoring all stakeholders. The primacy of insiders over the general public proved, in this case, dangerous even to the insiders themselves, at least in the short run. Decades later, thanks to the Abe administration's antideflationary monetary policy, cranes once again spike over Tokyo's skyline, and "Mori" skyscrapers count in the dozens in glitzy uptown neighborhoods. The reader is left wondering if the system has recalibrated, or if cheap money once again hides underlying rigidities. However, the US's own financial cataclysm in 2008, worse for the world than Japan's because of greater global financial integration, showed the limits of even US-style regulation, which purports to place more of the costs of financial stability on financial institutions themselves. US banks...

PurposeEnhanced risk management through the application of mathematical optimization is the next competitive‐advantage frontier for the primary‐insurance industry. The widespread adoption of catastrophe models for risk management provides the opportunity to exploit mathematical optimization techniques to achieve superior financial results over traditional methods of risk allocation. The purpose of this paper is to conduct a numerical experiment to evaluate the relative performances of the steepest‐ascent method and genetic algorithm in the solution of an optimal risk‐allocation problem in primary‐insurance portfolio management.Design/methodology/approachThe performance of two well‐established optimization methods – steepest ascent and genetic algorithm – are evaluated by applying them to solve the problem of minimizing the catastrophe risk of a US book of policies while concurrently maintaining a minimum level of return.FindingsThe steepest‐ascent method was found to be functionally dependent on, but not overly sensitive to, choice of initial starting policy. The genetic algorithm produced a superior solution to the steepest‐ascent method at the cost of increased computation time.Originality/valueThe results provide practical guidelines for algorithm selection and implementation for the reader interested in constructing an optimal insurance portfolio from a set of available policies.

The problem of optimal capital and risk allocation among economic agents, has played a predominant role in the respective academic and industrial research areas for decades. Typically as risk occurs in face of randomness the risks which are to be measured are identified with real-valued random variables on some probability space (Ω, F, P). Consider a model space X , and n economic agents with initial endowments X1, · · · , Xn ∈ X who assess the riskiness of their positions by means of law-invariant convex risk measures ρi : X → (−∞,∞]. In order to minimize total and individual risk, the agents redistribute the aggregate endowment X = X1 + · · · + Xn among themselves. An optimal capital and risk allocation Y1, · · · , Yn satisfies Y1 + · · · + Yn = X and ρ1(Y1) + · · · + ρ(Yn) = inf nXn i=1 ρi(Xi) : Xi ∈ X , i = 1, . . . , n, and Xn i=1 Xi = X o , (0.1) where n i=1ρi(X) = inf nPn i=1 ρi(Xi) : Xi ∈ X , i = 1, . . . , n, and Pn i=1 Xi = X o is the inf-convolution of ρ1, ..., ρn. In 2008, Filipovi´c and Svindland proved that if X is an L p (P) for some 1 ≤ p ≤ ∞ and ρi satisfy a suitable continuity condition (i.e. Fatou property), then Problem (0.1) always admits a solution. To reflect the fact of randomness of risk, we should consider the model space X chosen for risk evaluations to be as general as possible. The main contribution of this thesis is Theorem 4.10 has been published in [9]. It extends Filipovi´c and Svindland’s result from L p spaces to general rearrangement invariant (r.i.) spaces.

Optimal allocation of risk between the public and private sector is instrumental to the enhancement of value-for-money (VFM) for public-private partnership (PPP) infrastructure projects. This study offers a novel method that considers the risk mitigation capability (RMC) of the public and private sector to evaluate VFM of a PPP infrastructure project under the performance-based annuity (PPP/AP) scheme. It is the first attempt to incorporate both the RMC and risk allocation decisions into VFM development quantitatively. This model applies a combination of the Takagi-Sugeno fuzzy inference system and statistical methods. The perceptional data from Indonesian PPP experts were collected to estimate model parameters and assess the VFM of a 73 km Indonesian public road, and then used to illustrate the application of the model. The result shows that moderate levels of RMC for both the public and private sector, worsened by suboptimal risk allocation, lead to a no-go decision with PPP/AP. The proposed model makes earlier PPP decision-making possible for the public sector before invitations for bids.

The Public-Private Partnerships Scheme (PPP) has become an important option in overcoming the gap in infrastructure financing needs. From the total number of PPP projects implemented in several countries, it was found that the number of small-scale PPP projects was relatively greater than mega PPP projects. In line with this, in the Indonesian context, regional governments are expected to be able to innovate infrastructure financing, including by using the PPP scheme. The Madiun Regency Street Lighting Equipment (APJ) PPP project is the first small-scale PPP that has completed the auction process and signed the Cooperation Agreement in Indonesia. Using the qualitative method through the relevant case study approach, this research succeeded in identifying several challenges as well as opportunities for more massive implementation potentials of small-scale PPP in APJ in the future as follows: (1) optimal risk allocations; (2) the strong commitment of the regional government as the party responsible for the cooperation project; (3) financial aspects/parameters accepted by the market; and (4) doable projects.

Problem description: In practice, many consumer products are produced and stocked in product lines rather than in single product variants. The issue is that manufacturers and retailers often do not agree on the product line length (i.e., the number of variants included in the product line). The focus of this study is to understand how product line length and stocking quantities depend on how demand risk is contractually allocated. Academic/practical relevance: Our model combines assortment and stocking decisions in the presence of stochastic demand; previous models could address either assortment or stocking issues, but not necessarily both. Methodology: We present a game-theoretic model of a bilateral supply chain in which a manufacturer (he) sells up to two differentiated products through a retailer (she). He decides which products to produce, their wholesale prices, and how to allocate demand risk. We theorize that he can either retain the risk (by adopting a pull contract) or that he can pass it onto the retailer (by adopting a push contract). She responds by choosing assortment, quantities, and retail prices. By solving the model, we develop a descriptive theory that clarifies his incentive to expand his product offering and to reallocate demand risk within the supply chain. Results: Depending on the level of product differentiation, we identify three regions. When product differentiation is either low (commodities) or high (specialized products), the contract choice affects order quantities but not assortment. In these regions, the manufacturer’s contract choice can be explained by looking at elasticity of wholesale demand. For products with some differentiation, the manufacturer’s contract choice affects both order quantities and assortment. In this region, the manufacturer’s contract choice can be explained by looking at the additive effect of demand elasticity and sales expansion from the extended product line net of cannibalization. Managerial implications: Our paper can be seen as a first step toward developing a link between optimal product line design and optimal risk allocation in a bilateral supply chain.

This article builds on Froot and Stein in developing a framework for analyzing the risk allocation, capital budgeting, and capital structure decisions facing insurers and reinsurers. The model incorporates three key features: (i) value‐maximizing insurers and reinsurers face product‐market as well as capital‐market imperfections that give rise to well‐founded concerns with risk management and capital allocation; (ii) some, but not all, of the risks they face can be frictionlessly hedged in the capital market; and (iii) the distribution of their cash flows may be asymmetric, which alters the demand for underwriting and hedging. We show these features result in a three‐factor model that determines the optimal pricing and allocation of risk and capital structure of the firm. This approach allows us to integrate these features into: (i) the pricing of risky investment, underwriting, reinsurance, and hedging; and (ii) the allocation of risk across all of these opportunities, and the optimal amount of surplus capital held by the firm.

Portfolio optimization under conditions of risk and market uncertainty remains a foundational challenge in financial economics and investment management. Classical optimization frameworks, including mean–variance models and stochastic programming approaches, often struggle with high-dimensional asset universes, nonlinear correlations, and dynamic market regimes. This paper examines quantum computing approaches to portfolio optimization under risk and market uncertainty, focusing on hybrid quantum–classical algorithms designed to enhance combinatorial optimization and probabilistic modeling. By integrating quantum annealing, variational quantum circuits, and quantum-enhanced sampling techniques with classical financial analytics, the study evaluates their potential to improve computational efficiency and scenario sensitivity. The analysis considers both theoretical advantages and practical limitations within the Noisy Intermediate-Scale Quantum (NISQ) era. The findings suggest that quantum-assisted optimization may complement traditional portfolio models by expanding feasible solution spaces and improving robustness under uncertainty, thereby contributing to more adaptive and resilient investment strategies.

As financial crises became more frequent during recent decades, so also have books about them, as well as about crises that occurred centuries earlier. These studies tend to come in three styles: (1) narratives of one or more crises, usually by historians and journalists; (2) financial-economic-heuristic models of the typical patterns or essential stages of crises, as illustrated by historical examples, often adduced by financial economists with historical interests; and (3) large-scale data assemblies and econometric analyses covering decades or centuries of crises by economists.1Boom and Bust, written by two financial economists who observed firsthand from their posts in Belfast the devastating effects of the global financial crisis from 2007 to 2009 on Ireland, combines styles 1 and 2. The authors call their simple model “the bubble triangle.” Its three sides (with analogies to a fire) are marketability (oxygen), money and credit (fuel), and speculation (heat). Financial bubbles form when it is easy to buy and sell assets, when ample money and credit is available to finance speculative purchases, and when people are in a mood to speculate. These, however, are only necessary conditions for a bubble. They become sufficiently hot to inflate a bubble only with the right spark, which the authors contend can come from either of two sources, a captivating technological breakthrough (for example, the internet leading to the “dot com” bubble) or governmental policies that cause a rise in asset prices (for example, home-ownership policies leading to the sub-prime bubble).The authors develop narratives of several bubbles and then analyze each of them using their bubble-triangle framework. Some of the cases—the Mississippi and South Sea bubbles of 1719/20, the British railway mania of the 1840s, the Wall Street stock bubble of the late 1920s, Japan’s stock and real-estate bubble of the 1980s, and the recent “dot com” and sub-prime bubbles—are familiar to financial historians. Others such as the Australian real-estate bubble of the 1880s and the British bicycle mania of the 1890s are more obscure.The book’s discussion and analysis of two stock-market bubbles in China, in 2007 and 2015, is particularly useful because these bubbles are recent and not well known. In each instance, the Chinese authorities engineered a bubble to advance a policy goal. In 2007, the authorities wanted to privatize government-owned untraded shares in state-owned enterprises into privately owned tradable shares, and a bubble eased achievement of the goal. In 2015, after encouraging massive private-sector borrowing to alleviate the impact of the global crisis from 2007 to 2009, China’s authorities hoped that a new stock bubble would allow companies to raise equity capital on easy terms and use it to reduce their bloated debts. China’s 2015 bubble promoted debt for equity swaps to ease corporate debt burdens in the same way that John Law’s Mississippi bubble and the South Sea Company’s bubble did in 1719/20 to ease the debt burdens of the French and British governments. Financial history is cyclical, forever blowing bubbles.Quinn and Turner tout their model as predictive. A test of its predictive power seems underway (as of mid-2021), when the S&amp;P 500 stock index hit an all-time high. All the authors’ necessary conditions for a bubble scenario appear to be in place. Competition of financial firms for assets and trades has made the marketability of stocks and other assets easier and cheaper than ever before. The Federal Reserve roughly doubled its balance sheet over the past year, vastly expanding the supply of money and credit. To fight the economic slowdown caused by the Covid-19 pandemic, Congress enacted trillions of dollars of fiscal stimulus, with more on the way. Signs of speculative excesses abound, with names such as Archegos, Bitcoin, Credit Suisse, GameStop, Greensill, non-fungible tokens (nfts), Nomura, Reddit, Robinhood, and special-purpose acquisition companies (spacs) attached to them. So far, none of these potential sparks has started the deflation of a bubble, if indeed there is one in mid-2021. Conventional wisdom, challenged by Quinn and Turner, holds that we can know a bubble only after it bursts. By the time this review is published, we may have some test results.

Health status and portfolio choice: Is their relationship economically relevant?