Optimal Investment and Proportional Reinsurance with Risk Constraint

Abstract

In this paper, we investigate the problem of maximizing the expected exponential utility for an insurer. In the problem setting, the insurer can invest his/her wealth into the market and he/she can also purchase the proportional reinsurance. To control the risk exposure, we impose a value-at-risk constraint on the portfolio, which results in a constrained stochastic optimal control problem. It is difficult to solve a constrained stochastic optimal control problem by using traditional dynamic programming or Martingale approach. However, for the frequently used exponential utility function, we show that the problem can be simplified significantly using a decomposition approach. The problem is reduced to a deterministic constrained optimal control problem, and then to a finite dimensional optimization problem. To show the effectiveness of the approach proposed, we consider both complete and incomplete markets; the latter arises when the number of risky assets are fewer than the dimension of uncertainty. We also conduct numerical experiments to demonstrate the effect of the risk constraint on the optimal strategy.

The Optimal Investment and Re-Guarantee Purchase of China’s Financing Guarantee Institutions Considering Risk Preference

“…As for the selection of optimization criteria, the following categories of criteria are widely used. The first is to minimize the probability of bankruptcy of the company, that is, to minimize the company's operational risk by formulating the optimal investment portfolio and reinsurance strategies [21]. The second is the mean-variance criterion, which converts the bi-objective planning problem of minimizing risk and maximizing expected utility into a single-objective decision model through a linear combination method, and maximizes the utility of the company by determining the ratio of investment and reinsurance [22][23].…”

Discrete-Time Nonlinear Stochastic Optimal Control Problem Based on Stochastic Approximation Approach

“…Further from this, the state estimate shall be used to optimize and control the dynamical system, where the optimal control policy is drawn apparently [1] [2] [3] [4] [5]. From literatures, the applications of the nonlinear stochastic optimal control are widely studied, see for examples, vehicle trajectory planning [6], portfolio selection problem [7], building structural system [8], investment in insurance [9], switching system [10], machine maintenance problem [11], nonlinear differential game problem [12], and viscoelastic systems [13].…”

Optimal investment-reinsurance policy with regime switching and value-at-risk constraint

“…They define the MVaR constraint as the maximum value of the VaRs over different regimes. In addition, quite a few papers focus on the optimal strategies for the insurance company with the VaR constraint, such as [15], [16], and [7]. In [7], Chen et al investigate the optimal investmentreinsurance policy for an insurance company with a dynamic VaR constraint.…”