ABSTRACT This study develops a novel multivariate stochastic framework for assessing systemic risks, such as climate and nature‐related shocks, within production or financial networks. By embedding a linear stochastic fluid network, interpretable as a generalized vector Ornstein–Uhlenbeck process, into the production network of interdependent industries, the model captures how physical shocks (e.g., extreme climate events or geopolitical disruptions) propagate through input–output (IO) linkages and affect sectoral price dynamics. The framework extends traditional IO models with advanced stochastic and dynamic features, enabling a quantification of both direct and indirect transmission channels of supply‐cost shocks to production prices. Contributing to the literature on stochastic IO and Markovian networks, the model introduces the concept of divisible shocks, allowing for finer‐grained simulation of adaptation responses and resilience across sectors. Empirical calibration leverages real‐world economic data, including IO tables and historical industrial price indices. Sensitivity analyses are conducted using distributional risk measures, offering new tools for climate stress testing and medium to long‐term risk assessment. Our findings support the optimal design of supply risk management strategies, including policy interventions and decentralized adaptation incentives for systemic stability under environmental stress.

ABSTRACT We introduce a dynamic and stochastic interbank model with an endogenous notion of distress contagion, arising from rational worries about future defaults and ensuing losses. This entails a mark‐to‐market valuation adjustment for interbank claims, leading to a forward‐backward approach to the equilibrium dynamics whereby future default probabilities are needed to determine today's balance sheets. Distinct from earlier models, the resulting distress contagion acts, endogenously, as a stochastic volatility term that exhibits clustering and down‐market spikes. Furthermore, by incorporating multiple maturities, we provide a novel framework for constructing systemic interbank term structures, reflecting the intertemporal risk of contagion. We present the analysis in two parts: first, the simpler single maturity setting that extends the classical interbank network literature and, then, the multiple maturity setting for which we can examine how systemic risk materializes in the shape of the resulting term structures.

ABSTRACT Call option prices in the Black–Scholes model, viewed as functions of strike and maturity, are totally positive of order two (), meaning that the price ratio of a higher‐strike call to a lower‐strike call increases with maturity, with adjustments for dividends and interest. We develop conditions for this property in other models and contrast it with full total positivity, which holds only for out‐of‐the‐money strikes in the Black–Scholes model. Related properties apply to puts. We give a simple sufficient condition for based on the unimodality of ratios of densities of the underlying asset at different dates. We show that the property entails a strengthening of monotonicity of the underlying asset in the convex order and thus a strengthening of the absence of static arbitrage. We construct examples illustrating the gaps between these properties. We develop connections between and the shape of the implied volatility surface—in particular, connections with supermodularity of implied variance, a condition implying that lines of implied variance for different maturities fan out at high strikes. An examination of S&P 500 options market data indicates that violations are infrequent and typically reverse quickly.

ABSTRACTThis paper investigates the optimal investment problem in a market with two types of illiquidity: transaction costs and search frictions. We analyze a power‐utility maximization problem where an investor encounters proportional transaction costs and trades only when a Poisson process triggers trading opportunities. We show that the optimal trading strategy is described by a no‐trade region. We introduce a novel asymptotic framework applicable when both transaction costs and search frictions are small. Using this framework, we derive explicit asymptotics for the no‐trade region and the value function along a specific parametric curve. This approach unifies existing asymptotic results for models dealing exclusively with either transaction costs or search frictions.

ABSTRACTIn this work, we introduce a novel pricing methodology in general, possibly non‐Markovian local stochastic volatility (LSV) models. We observe that by conditioning the LSV dynamics on the Brownian motion that drives the volatility, one obtains a time‐inhomogeneous Markov process. Using tools from rough path theory, we describe how to precisely understand the conditional LSV dynamics and reveal their Markovian nature. The latter allows us to connect the conditional dynamics to so‐called rough partial differential equations (RPDEs), through a Feynman–Kac type of formula. In terms of European pricing, conditional on realizations of one Brownian motion, we can compute conditional option prices by solving the corresponding linear RPDEs, and then average over all samples to find unconditional prices. Our approach depends only minimally on the specification of the volatility, making it applicable for a wide range of classical and rough LSV models, and it establishes a PDE pricing method for non‐Markovian models. Finally, we present a first glimpse at numerical methods for RPDEs and apply them to price European options in several rough LSV models.

Abstract We prove a version of the fundamental theorem of asset pricing (FTAP) in continuous time that is based on the strict no‐arbitrage condition and that is applicable to both frictionless markets and markets with proportional transaction costs. We consider a market with a single risky asset whose ask price process is higher than or equal to its bid price process. Neither the concatenation property of the set of wealth processes, that is used in the proof of the frictionless FTAP, nor some boundedness property of the trading volume of admissible strategies usually argued within models with a nonvanishing bid–ask spread need to be satisfied in our model.

Abstract This paper addresses a continuous‐time contracting model that extends Sannikov's problem. In our model, a principal hires a risk‐averse agent to carry out a project. Specifically, the agent can perform two different tasks, namely to increase the instantaneous growth rate of the project's value, and to reduce the likelihood of accidents occurring. In order to compensate for these costly actions, the principal offers a continuous stream of payments throughout the entire duration of a contract, which concludes at a random time, potentially resulting in a lump‐sum payment. We examine the consequences stemming from the introduction of accidents, modeled by a compound Poisson process that negatively impact the project's value. Furthermore, we investigate whether certain economic scenarii are still characterized by a golden parachute as in Sannikov's model. A golden parachute refers to a situation where the agent stops working and subsequently receives a compensation, which may be either a lump‐sum payment leading to termination of the contract or a continuous stream of payments, thereby corresponding to a pension.