This paper investigates the optimal surplus management problem of an insurance company operating in a financial market with stochastic interest rates and jump-driven liabilities. The insurer dynamically allocates its surplus between a risky stock and a risk-free zero-coupon bond while facing insurance claims modeled by a compound Poisson process with exponentially distributed claim sizes. The short term interest rate follows a Cox-Ingersoll-Ross (CIR) process, which captures mean-reverting dynamics commonly observed in term structure models. The insurer maximizes the expected exponential utility of terminal surplus. Using stochastic control techniques, we derive the associated Hamilton-Jacobi-Bellman (HJB) equation. Although the exponential utility structure suggests an exponential affine representation, the interaction between the interest rate hedge and the surplus state generates quadratic surplus terms in the HJB equation. To obtain a tractable formulation, we adopt a normalized surplus projection method, which provides an approximate reduction of the full three-dimensional problem to a nonlinear system of partial differential equations (which is subsequently numerically validated). The optimal investment policy admits an economically meaningful decomposition consisting of a myopic demand component and an interest rate hedging component. Numerical experiments illustrate how the optimal strategy and the surplus distribution depend on interest rate volatility, claim intensity, and risk aversion. The results highlight the importance of jointly modeling stochastic interest rates and insurance liability risk when designing optimal investment policies for insurance companies.
We study equilibrium price formation in an incomplete financial market with a large population of agents, where stock prices are subject to a single-default event. Agents are assumed to be heterogeneous in their risk aversion and terminal liabilities, and maximize exponential utility of terminal net wealth. We first characterize each agent's optimal strategy by a quadratic-growth backward stochastic differential equation (BSDE) driven by Brownian motions and a compensated default martingale. We then formulate the market-clearing condition in terms of aggregate optimal demand and derive a mean-field quadratic-growth BSDE for the equilibrium risk premium. The resulting characterization quantifies how default intensity, jump size, and agent heterogeneity jointly shape the default-risk component of equilibrium security risk premia. Under a Markovian factor model, we establish short-time solvability of the mean-field BSDE through a fixed-point argument based on estimates for a coupled semilinear PDE system. Finally, we show that the risk premium characterized by the mean-field BSDE asymptotically clears the market as the population size tends to infinity.
The Reverse Kelly Automated Market Maker (rkAMM) is introduced, the core engine of the proposed lending framework for decentralized credit and provides the foundational financial engineering required to bridge the 2 trillion global supply chain finance gap using permissionless blockchain infrastructure.
Sai Srikanth Madugula, Peplluis Esteva de la Rosa, Daya Shankar· 0 citations
We study dynamic physical hedging for insurers exposed jointly to catastrophe losses and stochastic reconstruction costs. Surplus evolves as a controlled jump diffusion whose loss amplitude combines marked catastrophe severity, an exogenous mean-reverting cost factor, and endogenous mitigation. We establish well-posedness, moment and stability estimates, and a stopping-time dynamic programming principle, and prove that the value function is the unique viscosity solution of the resulting nonlocal Hamilton-Jacobi-Bellman (HJB) equation Strategic interaction is introduced through a mean field game (MFG) with reduced-form vulnerability costs, yielding a coupled backward-forward HJB-Kolmogorov system. We establish relaxed equilibrium existence, Markovian realization, and uniqueness under appropriate compactness and monotonicity conditions. Numerical experiments show that reconstruction costs and capitalization materially affect optimal hedging and that cross-sectional vulnerability alters equilibrium costs. Tail-family robustness calculations further assess the sensitivity of these conclusions to alternative catastrophe-severity specifications.
We develop a structural credit-risk model under incomplete information in which investors observe firm value only indirectly through noisy market signals and scheduled corporate disclosures. While disclosure dates are known in advance, their informational content is random, leading to stochastic discontinuities in the observation process. We derive the Kushner-Stratonovich equation for structural credit-risk models with endogenous default by applying the nonlinear filtering framework with predictable jumps. We then study the valuation and local risk-minimization hedging for default-sensitive securities under partial information. The interaction between predictable disclosure events and endogenous default produces discrete adjustments in the conditional default compensator, leading to announcement-driven distortions in credit spreads and hedge ratios that are absent from classical diffusion-based and inaccessible-jump models. Numerical experiments illustrate how scheduled disclosures affect filtered default probabilities, Credit Default Swaps (CDS) spreads, and hedging strategies, generating characteristic pre-announcement dynamics in credit spreads.
We develop a continuous-time structural dynamic model to determine the exact insolvency regions of banks arising from the non-linear interaction between liquidity and credit risk. While existing literature predominantly treats these risks in isolation or via reduced-form specifications, we explicitly model the feedback loop where funding shocks and regulatory constraints force balance-sheet adjustments that can lead to endogenous insolvency. By incorporating Basel III regulatory requirements (LCR and NSFR) into a stochastic optimal control framework, we solve for the exact insolvency boundary using the Hamilton-Jacobi-Bellman (HJB) equation. To bridge the gap between theoretical complexity and supervisory practice, we derive and validate a surrogate analytical approximation function that allows for real-time monitoring. Calibrated using granular balance-sheet data from the Iranian banking sector, our model reveals significant non-linear threshold effects: the joint occurrence of liquidity stress and credit portfolio defaults disproportionately accelerates the transition toward insolvency compared to their individual effects. The proposed surrogate function offers supervisors a computationally efficient tool for stress testing and early warning systems. Our findings provide novel insights into financial frictions in emerging markets and offer a rigorous framework for integrated risk management.
This paper develops a multi-agent equilibrium model in an incomplete market setting. The model incorporates dividend-paying securities whose dividend processes are interpreted as flows of consumption goods and can be driven by exogenously given factor processes. We consider an optimal consumption and portfolio problem for agents who have different views on fundamental risks and heterogeneous time preferences. Using a convex duality approach, we obtain expressions for the equilibrium state price density process, which subsequently yields the term structure of discount rates. To better reflect market practices, the model also incorporates discrete timing for dividend payments, consistent with semiannual or annual coupon schedules and policy decisions that typically occur at specific points during the year. As an application of the model, we provide numerical examples of long-term discount rates for valuing long-dated cashflows while exogenously incorporating the dynamics of factor processes that drive the dividend processes reflecting changes in the amount of government bonds available in the market. We examine how changes in the supply of government bonds affect the pricing of insurance products, including death benefits and pension annuities, through shifts in long-term discount rates. The numerical examples illustrate the qualitative implications of the model and are not intended to provide empirical findings.