arXiv subjects

Jian-hao Kang

Publications and source records attributed to Jian-hao Kang.

6 recordsLinked to original sources

arXiv2026

Time-inconsistent reinsurance and investment optimization problem with delay under random risk aversion

This paper considers a newly delayed reinsurance and investment optimization problem incorporating random risk aversion, in which an insurer pursues maximization of the expected certainty equivalent of her/his terminal wealth and the cumulative delayed information of the wealth over a period. Specially, the insurer's surplus dynamics are approximated using a drifted Brownian motion, while the financial market is described by the constant elasticity of variance (CEV) model. Moreover, the performance-linked capital flow feature is incorporated and the wealth process is formulated via a stochastic delay differential equation (SDDE). By adopting a game-theoretic approach, a verification theorem with rigorous proofs is established to capture the equilibrium reinsurance and investment strategy along with the equilibrium value function. Furthermore, analytical or semi-analytical equilibrium reinsurance and investment strategies, together with their equilibrium value functions, are obtained under the CEV model for the exponential utility and derived under the Black-Scholes model for both exponential and power utilities. Finally, several numerical experiments are conducted to analyze the behavioral characteristics of the freshly-derived equilibrium reinsurance and investment strategy.

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arXiv2025

Equilibrium reinsurance and investment strategies for insurers with random risk aversion under Heston's SV model

This study employs expected certainty equivalents to explore the reinsurance and investment issue pertaining to an insurer that aims to maximize the expected utility while being subject to random risk aversion. The insurer's surplus process is modeled approximately by a drifted Brownian motion, and the financial market is comprised of a risk-free asset and a risky asset with its price depicted by Heston's stochastic volatility (SV) model. Within a game theory framework, a strict verification theorem is formulated to delineate the equilibrium reinsurance and investment strategies as well as the corresponding value function. Furthermore, through solving the pseudo Hamilton-Jacobi-Bellman (HJB) system, semi-analytical formulations for the equilibrium reinsurance and investment strategies and the associated value function are obtained under the exponential utility. Additionally, several numerical experiments are carried out to demonstrate the characteristics of the equilibrium reinsurance and investment strategies.

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arXiv2024

Consumption and portfolio optimization solvable problems with recursive preferences

This paper considers consumption and portfolio optimization problems with recursive preferences in both infinite and finite time regions. Specially, the financial market consists of a risk-free asset and a risky asset that follows a general stochastic volatility process. By using Bellman's dynamic programming principle, the Hamilton-Jacobi-Bellman (HJB) equation is derived for characterizing the optimal consumption-investment strategy and the corresponding value function. Based on the conjecture of the exponential-polynomial form of the value function, we prove that, when the order of the polynomial $n\leq2$, the HJB equation has an analytical solution if the investor with unit elasticity of intertemporal substitution (EIS) and an approximate solution otherwise.

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arXiv2024

Stochastic Linear-quadratic Control Problems with Affine Constraints

This paper investigates the stochastic linear-quadratic control problems with affine constraints, in which both equality and inequality constraints are involved. With the help of the Pontryagin maximum principle and Lagrangian duality theory, the dual problem of original problem is established and the state feedback form of the solution to the optimal control problem is obtained. Under the Slater condition, the equivalence is proved between the solutions to the original problem and the ones of the dual problem, and the KKT condition is also provided for solving original problem. Especially, a new sufficient condition is given for the invertibility assumption, which ensures the uniqueness of the solutions to the dual problem.

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arXiv2024

Optimal Control Problems Governed by MFSDEs with multi-defaults

In this paper, we solve an optimal control problem governed by a system of mean-field stochastic differential equations with multiple defaults (MMFSDEs). We transform the global optimal control problem into several optimal control subproblems governed by a system of mean-field stochastic differential equations with single default (SMFSDEs) and derive both the sufficient and necessary maximum principles for these subproblems. We also give the existence and uniqueness of solutions to the MMFSDEs and the mean-field backward stochastic differential equations with multiple defaults (MMFBSDEs), respectively. Finally, as an example, our results are applied to obtain the explicit solution for an optimal control problem whose cost function is considered as a recursive utility process with multiple defaults.

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arXiv2022

Robust equilibrium strategy for mean-variance-skewness portfolio selection problem

This paper considers a robust time-consistent mean-variance-skewness portfolio selection problem for an ambiguity-averse investor by taking into account wealth-dependent risk aversion and wealth-dependent skewness preference as well as model uncertainty. The robust equilibrium investment strategy and corresponding equilibrium value function are characterized for such a problem by employing an extended Hamilton-Jacobi-Bellman-Isaacs (HJBI) system via a game theoretic approach. Furthermore, the robust equilibrium investment strategy and corresponding equilibrium value function are obtained in semi-closed form for a special robust time-consistent mean-variance-skewness portfolio selection problem. Finally, some numerical experiments are provided to indicate several new findings concerned with the robust equilibrium investment strategy and the utility losses.

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