Linear reflected backward stochastic differential equations arising from vulnerable claims in markets with random horizon.

We consider a financial framework with two levels of information: the public information generated by the financial assets, and a larger flow of information that contains additional knowledge about a random time. This random time can represent many economic and financial settings, such as the default time of a firm for credit risk, and the death time of an insured for life insurance. As the random time cannot be seen before its occurrence, the progressive enlargement of filtration seems tailor‐fit to model the larger flow of information that incorporates both the public flow and the information about the random time. In this context, our interest focuses on the following challenges: (a) How to single out the various risks coming from the financial assets, the random time, and their correlations? (b) How these risks interplay and lead to the formation of any risk in the larger flow of information? It is clear that understanding how risks build‐up and interact, when one enlarges the flow of information, is vital for an efficient risk management and derivatives' evaluation in those informational markets. Our answers to these challenges are full and complete no matter what the model for the random time is and no matter how the random time is related to the public flow. In fact, we introduce “pure default” risks, and quantify and classify these risks afterward. Then we elaborate our martingale representation results, which state that any martingale in the large filtration stopped at the random time can be decomposed into orthogonal local martingales (i.e., local martingales whose product remains a local martingale). This constitutes our first principal contribution, while our second contribution consists in evaluating various defaultable securities according to the recovery policy, within our financial setting that encompasses any default model, using a martingale “basis.” Our pricing formulas explain the impact of various recovery policies on securities and determine the types of pure default risk they entail.

Infinite horizon optimal control problem of mean-field backward stochastic delay differential equation under partial information

ABSTRACTIn this article, we consider an optimization problem of expected utility maximization of continuous-time trading in a financial market. This trading is constrained by a benchmark for a utility-based shortfall risk measure. The market consists of one asset whose price process is modelled by a Geometric Brownian motion where the market parameters change at a random time. The information flow is modelled by initially and progressively enlarged filtrations which represent the knowledge about the price process, the Brownian motion and the random time. We solve the maximization problem and give the optimal terminal wealth depending on these different filtrations for general utility functions by using martingale representation results for the corresponding filtration.

Motivated by structural, reduced-form and hybrid models of the third party and counterparty credit risk, we study a generalized backward stochastic differential equations (BSDE) up to a random time horizon ϑ, which is not a stopping time with respect to a reference filtration. In contrast to the existing literature in the area of credit risk modeling, we do not impose specific assumptions on the random time ϑ and we study the existence of solutions to BSDE and reflected BSDE with a random time horizon through the method of reduction. For this purpose, we also examine BSDE and reflected BSDE with a làdlàg driver where the driver is allowed to have a finite number of jumps overlapping with jumps of the martingale part. Theoretical results are illustrated by particular instances of a random time and explicit BSDEs in either the Brownian or Brownian-Poisson filtration.

The study examines the variables associated with the amount and type of life insurance purchased by a sample of young newly-married couples. Socioeconomic, demographic, psychographic, and other variables are examined by means of Multiple Classification Analysis. The purchase of a larger than average amount of life insurance was found to be much more likely in households where: (1) the husband did not attend college, (2) current and expected household incomes were in the low and high ranges, (3) net worth was greater, (4) the husband had purchased no life insurance before marriage, and (5) the wife had purchased term insurance before marriage. The purchase of term insurance was found to be much more likely in households where: (1) the net worth was greater, (2) the wife purchased term insurance before marriage, and (3) the insurance agent did not influence the decision. The purchase of life insurance is one of the most important consumer purchasing decisions. In the United States, consumers pay out over $24 billion for life insurance premiums or slightly over three percent of their total disposable personal income. These premium receipts, plus the investment income earned on them, has allowed the life insurance industry to become one of the most powerful financial institutions, controlling over $240 billion in assets. One of the most important market segments for the life insurance industry consists of young married couples. Often the first and most important purchases of life insurance are made at this stage of the life cycle. Life insurance decisions made at this time may have a lasting influence on future life insurance purchases. Thus, it is important for the industry to understand the life insurance purchasing behavior of this market segment. This article examines the variables associated with the amount and the type of life insurance purchased by young newly-married couples. Socioeconomic variables, demographic variables, psychographic variables, and other explanatory factors, some of which have not been investigated Dan R. Anderson, Ph.D., CPCU, is Assistant Professor of Business (Risk Management and Insurance) in the Graduate School of Business of the University of Wisconsin, Madison. John R. Nevin, Ph.D., is Assistant Professor of Business (Marketing) in the Graduate School of Business of the University of Wisconsin, Madison. This paper was submitted in April, 1974.

Recent research documents that exposure to air pollution can trigger various behavioral reactions. This article presents novel empirical evidence on the causal effect of pollution risk on life insurance decisions. We create a unique dataset by linking microgeographic air quality information to the confidential UK Wealth and Assets Survey. We identify an inverse N-shape relationship between pollution risk and life insurance adoption by exploiting the orthogonal variations in meteorological conditions. Over a given range above a threshold of exposure, rising pollution is associated with rising demand for life insurance, whereas at lower than the threshold levels of pollution, higher exposure risk reduces demand for insurance. Our findings indicate-for the first time-a nonlinear relationship between local pollution risk and life insurance demand.

The X-valuation adjustment (XVA) problem, which is a recent topic in mathematical finance, is considered and analyzed. First, the basic properties of backward stochastic differential equations (BSDEs) with a random horizon in a progressively enlarged filtration are reviewed. Next, the pricing/hedging problem for defaultable over-the-counter (OTC) derivative securities is described using such BSDEs. An explicit sufficient condition is given to ensure the non-existence of an arbitrage opportunity for both the seller and buyer of the derivative securities. Furthermore, an explicit pricing formula is presented in which XVA is interpreted as approximated correction terms of the theoretical fair price.

This work recommends and analyzes the most appropriate curricula for students in departments of risk management and insurance from the perspective of life insurance companies in Taiwan. The paper proposes a curriculum performance evaluation method combining the Analytical Hierarchy Process (AHP) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The AHP is used in obtaining the relative weights of criteria, and then the TOPSIS approach is employed to rank how universities perform in using this curriculum. Research results find that experts select the most appropriate curricula in universities for life insurance companies based on the following rankings: personal insurance, insurance company operations and management, and insurance theory and legal. The results suggest that Shih Chien University (SCU) provides the most appropriate curriculum and its students are the most employable graduates by life insurance companies in Taiwan. The proposed AHP-based algorithm significantly helps faculty in departments of risk management and insurance to improve their curriculum design. The proposed algorithm, which is objective and systematic in selection procedures, can help human resources managers recruit highly qualified graduates for their companies.

Underwriting is crucial for insurers’ performance and sustainability, yet empirical evidence on factors influencing its performance has received limited attention. Therefore, this study investigates this phenomenon considering South Africa’s life and non-life insurance sectors between 2013–2019. Using the generalized method of moments and the bootstrap quantile regression techniques for analysis, the findings show that insurance size, market share, and investment income significantly and positively impact underwriting performance. However, premium growth weakens the underwriting performance of both sectors. Also, non-life insurance shows a positive relationship for reinsurance, while life insurers present an inverse relationship. Underwriting risk negatively impacts non-life performance across quantiles, while life insurer risk was negative in higher quantiles. More so, initial solvency levels weaken underwriting performance, while extreme increase improves it, implying a direct U-shaped relationship. Hence, highly solvent insurers are more likely to succeed in underwriting operations. Additionally, market share complements return on assets in promoting underwriting performance. Policy recommendations are discussed.

Stability in distribution of neutral stochastic functional differential equations with Markovian switching

A fundamental problem in online query auditingis that an outside attacker may compromise database privacy by exploiting the sequence of query responses and the information flow from the database state to the auditing decision. Kenthapadi et al. [14] proposed the simulatable auditingmodel to solve this problem in a way that completely blocks the aforementioned information flow. However, the security does not come for free. The simulatable auditing model actually suffers from unnecessary data utility loss. We assert that in order to guarantee database privacy, blocking the information flow from the true database state to the auditing decision is sufficient but far from necessary. To limit the loss in data utility, we suggest an alternative approach that controls, instead of blocks, such information flow. To this end, we introduce a new model, called simulatable binding, in which the information flow from the true database state to the auditing decision is provably controlled by a selected safe binding. We prove that the proposed simulatable binding model provides a sufficient and necessary condition to guarantee database privacy, and therefore, algorithms based on our model will provide better data utility than algorithms based on the simulatable auditing model. To demonstrate the strength and practicality of our model, we provide two efficient algorithms for the max query and sum query auditing, respectively. For the ease of comparison, each algorithm is built by applying our simulatable binding model, and is compared to an algorithm applying the simulatable auditing model. Clear improvements are shown through experiments.

The article is aimed at researching the main indicators of the activities of insurance companies in Ukraine and determining their role in the structure of credit system. Generalizing scientific works on the research issues of the functioning of non-bank financial and credit institutions as a whole and insurance companies in particular, the authors determine the need to study certain issues of development of insurance market actors at the present stage (namely, indicators of the activities of insurance companies) and define their place in the credit system. Analyzing the dynamics and structure of the assets of the credit system in the context of its components – the banking and parabanking system, the bank-centric model of the financial market is determined, because the main share in the assets of the credit system is occupied by the assets of banking institutions. It is determined that financial and insurance companies play a significant role in the functioning of the credit system of Ukraine among parabanking institutions. The analysis of the main indicators of the activity of insurance companies and the dynamics of their number is carried out. It is found that despite the decrease in the number of insurance companies in dynamics, the volumes of gross insurance premiums and gross insurance payments are characterized by positive growing trends. Factors influencing such changes are the exit from the market of unreliable and financially insolvent insurers; change of views on life insurance, assets and liability, as well as an active development of partnerships with foreign counterparties and the emergence of insurance companies with foreign capital on the domestic market. The article also provides a rating of insurance companies by assets at the end of 2020 and defines their share in the assets of the credit system in general. Prospects for further research are to distinguish the main reasons for the downturn in the number of insurers and their impact on the state of the financial services market as a whole.

Introduction. It is emphasized that the sustainable development of national economy is possible as long as the financial services market functions effectively. The market is formed by the entities providing insurance, banking and investment services.Purpose. The purpose of the article is to identify the current challenges which hinder the development of Ukraine’s financial services market.Methods. The methodological framework of the study includes the following general research methods: induction, analysis, and generalization.Results. The main indicators reflecting the performance of the domestic insurance services market are analysed. Based on gross insurance premiums and insurance payments, it is found out that the most common type of insurance is vehicle insurance. The research paper claims that nowadays various types of insurance are being developed progressively in Ukraine. Special attention is paid to life insurance, because this type of insurance is viewed as socially essential. However, the development of life insurance market in Ukraine is rated as low.The presence of domestic banks on the financial services market is determined through the following indicators: the amount of funds received by business entities and individuals; the amount of gross loans granted to them. Under the current conditions, the domestic banks are providing financial services with innovative solutions.The main performance indicators of the domestic market of investment services with the participation of joint investment institutions are analysed. The development of this segment of the investment services market is evidenced by the increasing volume of assets owned by investment funds. The author also notes that there is a lack of people’s involvement in joint investment institutions.Discussion. The research findings are applicable and can be used in implementing strategies for the growth of Ukraine’s financial services market.

Considerably much work has been done on Backward Stochastic Differential Equations (BSDEs) in continuous-time with deterministic terminal horizon or stopping times. Various new models have been introduced in these years in order to generalize BSDEs to solve new practical financial problems.
\nOne strand is focused on discrete-time models. Backward Stochastic Difference Equations (also called BSDEs if no ambiguity) on discrete-time finite-state space were introduced by Cohen and Elliott (2010a). The associated theory required only weak assumptions. In the first topic of this thesis, properties of non-linear expectations defined using the discrete-time finite-state BSDEs were studied. A converse comparison theorem was established. Properties of risk measures defined by non-linear expectations, especially the representation theorems, were given. Then the theory of BSDEs was applied to optimal design of dynamic risk measures. Another strand is about a general random terminal time, which is not necessarily a stopping time. The motivation of this model is a financial problem of hedging of defaultable contingent claims, where BSDEs with stopping times are not applicable. In the second topic of this thesis, discrete-time finite-state BSDEs under progressively enlarged filtration were considered. Martingale representation
\ntheorem, existence and uniqueness theorem and comparison theorem were established. Application to nonlinear expectations was also explored. Using the theory of BSDEs, the explicit solution for optimal design of dynamic default risk measures was obtained.
\nIn recent work on continuous-time BSDEs under progressively enlarged filtration, the reference filtration is generated by Brownian motions. In order to deal with cases with jumps, in the third topic of this thesis, a general reference filtration with predictable representation property and an initial time with immersion property were considered. The martingale representation theorem for square-integrable martingales under progressively enlarged filtration was established. Then the existence and uniqueness theorem of BSDEs under enlarged filtration using Lipschitz continuity of the driver was proved. Conditions for a comparison theorem were also presented. Finally applications to nonlinear expectations and hedging of defaultable contingent claims on Brownian-Poisson setting were explored.

The paper is devoted to the existence of perpetual integral functionals for several classes of d-dimensional of stochastic processes . The method is very simple: we establish the conditions supplying that these functionals have a finite expectation. Examples of these classes include d-dimensional fractional Brownian motion having coordinates with the same Hurst index H, for which existence is established under the assumption . In particular, perpetual integral functionals exist for d-dimensional Brownian motion with d>2, compound Poisson process, Markov processes admitting densities of transitional probabilities. In the case of Brownian motion and fractional Brownian motion we establish that the perpetual integral functionals are not a constant a.s. if .