Aug 2026· Mathematics· Vol 14, pp. 3121· 0 citations· 39 references
Abstract
We develop a stochastic-control and mean field game framework for catastrophe insurance under stochastic replacement-cost risk. Insurer surplus follows a controlled jump diffusion in which catastrophe losses are scaled by an exogenous mean-reverting replacement-cost factor and attenuated through physical hedging. We establish well-posedness and stability of the controlled state process, derive a stopping-time dynamic programming principle, and characterize the value function as the unique viscosity solution of the associated nonlocal Hamilton–Jacobi–Bellman (HJB) equation. We then formulate strategic interaction among insurers through a coupled nonlocal HJB–Kolmogorov system and establish existence and uniqueness of mean field equilibrium under regularity and monotonicity conditions. The analysis quantifies how elevated replacement costs amplify catastrophe-loss exposure while physical hedging reduces it. Numerical results indicate stronger optimal hedging under high replacement-cost states and weak capitalization and quantify the equilibrium effects of industry-wide vulnerability.
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-posedn...
This paper is devoted to developing a framework for stochastic growth models with environmental risk, in which rare but catastrophic shocks interact with capital accumulation and pollution. Building on the Poisson point process formulation studied in arXiv:2511.13568, we extend the model to disasters driven by a marked...
We study an infinite-horizon stochastic control problem for the optimal exploitation of an exhaustible resource with unknown total reserves. Information is generated both endogenously through continued extraction without depletion and exogenously through an external information flow. This interaction makes the natural...
This paper extends the optimal investment control framework by incorporating fractional Brownian motion to capture long-range dependence and memory effects in asset prices. Replacing the standard Brownian component with a fractional Brownian motion governed by the Hurst parameter H with H∈(1/2,1), we employ the Wick–It...
We study a finite-horizon reversible investment problem in which a risk-neutral firm adjusts capacity at a proportional purchase cost and a lower salvage value under multi-factor geometric Brownian motion. Via the singular control--optimal switching correspondence, the marginal value of capacity solves a family of para...
Junkee Jeon, Takwon Kim, Jinwan Park et al.· 0 citations
We consider a problem of optimal proportional reinsurance-dividend distribution under a Brownian risk model, where both the drift and volatility coefficients are subject to endogenous regime-switching. Dividend payments are subject to fixed transaction costs. The problem is formulated as a two-dimensional stochastic co...
