scholarly journals Optimal per-loss reinsurance and investment to minimize the probability of drawdown

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xia Han ◽  
Zhibin Liang ◽  
Yu Yuan ◽  
Caibin Zhang
Keyword(s):  
Closed Form ◽  
Financial Market ◽  
Value Function ◽  
Risk Model ◽  
Investment Strategy ◽  
Insurance Company ◽  
Optimal Reinsurance ◽  
Claim Number ◽  
Common Shock ◽  
Insurance Business

<p style='text-indent:20px;'>In this paper, we study an optimal reinsurance-investment problem in a risk model with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component. We assume that the insurer can purchase per-loss reinsurance for each line of business and invest its surplus in a financial market consisting of a risk-free asset and a risky asset. Under the criterion of minimizing the probability of drawdown, the closed-form expressions for the optimal reinsurance-investment strategy and the corresponding value function are obtained. We show that the optimal reinsurance strategy is in the form of pure excess-of-loss reinsurance strategy under the expected value principle, and under the variance premium principle, the optimal reinsurance strategy is in the form of pure quota-share reinsurance. Furthermore, we extend our model to the case where the insurance company involves <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula> <inline-formula><tex-math id="M2">\begin{document}$ (n\geq3) $\end{document}</tex-math></inline-formula> dependent classes of insurance business and the optimal results are derived explicitly as well.</p>

Robust Optimal Investment-Reinsurance Strategies for a Jump-Diffusion Risk Model with Mean-reverting Stock Return

2021 ◽  
Vol 7 (6) ◽  
pp. 6100-6114
Author(s):  
Wu Yungao
Keyword(s):  
Financial Market ◽  
Stock Return ◽  
Value Function ◽  
Risk Model ◽  
Optimal Investment ◽  
Jump Diffusion ◽  
Insurance Companies ◽  
Insurance Company ◽  
Terminal Time ◽  
The Value Function

Objectives: This paper proposes a strategy of robust optimal investment reinsurance for insurance companies. It was assumed that the surplus procedure of the insurance company satisfies the jump-diffusion procedure. Insurance companies could invest their surplus funds in the financial market consisted of both risk assets and one risk-free asset. The price procedure of risk assets satisfies the stochastic procedure with a mean reversion rate. Considering the uncertainty of the model, the ambiguity-averse insurance firm aims to enhance the exponential utility of insurance surplus at terminal time. This paper has investigated the problem of robust optimal investment reinsurance and obtained the differential equation supported by the value function.

scholarly journals Optimal Reinsurance-Investment Problem under Mean-Variance Criterion with n Risky Assets

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Peng Yang
Keyword(s):  
Financial Market ◽  
Investment Strategy ◽  
Hjb Equation ◽  
Model Parameters ◽  
Optimal Reinsurance ◽  
Risky Assets ◽  
Terminal Wealth ◽  
Investment Problem ◽  
Mean Variance ◽  
Variance Criterion

Based on the mean-variance criterion, this paper investigates the continuous-time reinsurance and investment problem. The insurer’s surplus process is assumed to follow Cramér–Lundberg model. The insurer is allowed to purchase reinsurance for reducing claim risk. The reinsurance pattern that the insurer adopts is combining proportional and excess of loss reinsurance. In addition, the insurer can invest in financial market to increase his wealth. The financial market consists of one risk-free asset and n correlated risky assets. The objective is to minimize the variance of the terminal wealth under the given expected value of the terminal wealth. By applying the principle of dynamic programming, we establish a Hamilton–Jacobi–Bellman (HJB) equation. Furthermore, we derive the explicit solutions for the optimal reinsurance-investment strategy and the corresponding efficient frontier by solving the HJB equation. Finally, numerical examples are provided to illustrate how the optimal reinsurance-investment strategy changes with model parameters.

Optimal investment-reinsurance problems with common shock dependent risks under two kinds of premium principles

2019 ◽  
Vol 53 (1) ◽  
pp. 179-206
Author(s):  
Junna Bi ◽  
Kailing Chen
Keyword(s):  
Risk Model ◽  
Optimal Strategies ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Model Parameters ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Common Shock ◽  
The Impact ◽  
Poisson Risk Model

This paper considers the optimal investment-reinsurance strategy in a risk model with two dependent classes of insurance business under two kinds of premium principles, where the two claim number processes are correlated through a common shock component. Under the criterion of maximizing the expected exponential utility with the expected value premium principle and the variance premium principle, we use the stochastic optimal control theory to derive the optimal strategy and the value function for the compound Poisson risk model as well as for the Brownian motion diffusion risk model. In particular, we find that the optimal investment strategy on the risky asset is independent to the reinsurance strategy and the reinsurance strategy for the compound Poisson risk model are very different from those for the diffusion model under both two kinds of premium principles, but the investment strategies are the same in this two risk models. Finally, numerical examples are presented to show the impact of model parameters in the optimal strategies.

scholarly journals Optimal Reinsurance Problem under Fixed Cost and Exponential Preferences

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 295
Author(s):  
Matteo Brachetta ◽  
Claudia Ceci
Keyword(s):  
Optimal Stopping ◽  
Risk Model ◽  
Stopping Time ◽  
Fixed Cost ◽  
Model Parameters ◽  
Insurance Company ◽  
Optimal Reinsurance ◽  
Retention Level ◽  
Step Procedure ◽  
Time Problem

We investigate an optimal reinsurance problem for an insurance company taking into account subscription costs: that is, a constant fixed cost is paid when the reinsurance contract is signed. Differently from the classical reinsurance problem, where the insurer has to choose an optimal retention level according to some given criterion, in this paper, the insurer needs to optimally choose both the starting time of the reinsurance contract and the retention level to apply. The criterion is the maximization of the insurer’s expected utility of terminal wealth. This leads to a mixed optimal control/optimal stopping time problem, which is solved by a two-step procedure: first considering the pure-reinsurance stochastic control problem and next discussing a time-inhomogeneous optimal stopping problem with discontinuous reward. Using the classical Cramér–Lundberg approximation risk model, we prove that the optimal strategy is deterministic and depends on the model parameters. In particular, we show that there exists a maximum fixed cost that the insurer is willing to pay for the contract activation. Finally, we provide some economical interpretations and numerical simulations.

DYNAMIC PORTFOLIO SELECTION WITH UNCERTAINTY

2009 ◽  
Vol 17 (02) ◽  
pp. 237-250 ◽  
Author(s):  
MEI YU ◽  
HIROSHI INOUE ◽  
SATORU TAKAHASHI ◽  
JIANMING SHI
Keyword(s):  
Dynamic Programming ◽  
Closed Form ◽  
Portfolio Selection ◽  
Financial Market ◽  
Optimal Strategy ◽  
Investment Strategy ◽  
Selection Strategy ◽  
Total Risk ◽  
Dynamic Programming Problem ◽  
Dynamic Portfolio

How to make a prompt decision for uncertainty investment is always a key problem in financial market. In this paper, we present a new dynamic portfolio selection strategy in stock market. The investor is assumed to seek an investment strategy that will maximize his/her final wealth and minimize the total risk. An analytically optimal strategy in closed form is obtained by solving a dynamic programming problem. Some applications are also presented to illustrate this model.

scholarly journals Equilibrium reinsurance-investment strategy with a common shock under two kinds of premium principles

2021 ◽  
Author(s):  
Junna Bi ◽  
Danping Li ◽  
Nan Zhang
Keyword(s):  
Investment Strategy ◽  
Expected Value ◽  
Value Premium ◽  
Equilibrium Strategy ◽  
Model Parameters ◽  
Optimal Reinsurance ◽  
Investment Problem ◽  
Common Shock ◽  
Game Theoretic ◽  
Hamilton Jacobi Bellman

This paper investigates the optimal mean-variance reinsurance-investment problem for an insurer with a common shock dependence under two kinds of popular premium principles: the variance premium principle and the expected value premium principle. We formulate the optimization problem within a game theoretic framework and derive the closed-form expressions of the equilibrium reinsurance-investment strategy and equilibrium value function under the two different premium principles by solving the extended Hamilton-Jacobi-Bellman system of equations. We find that under the variance premium principle, the proportional reinsurance is the optimal reinsurance strategy for the optimal reinsurance-investment problem with a common shock, while under the expected value premium principle, the excess-of-loss reinsurance is the optimal reinsurance strategy. In addition, we illustrate the equilibrium reinsurance-investment strategy by numerical examples and discuss the impacts of model parameters on the equilibrium strategy.

Optimal proportional reinsurance with common shock dependence to minimise the probability of drawdown

2018 ◽  
Vol 13 (2) ◽  
pp. 268-294 ◽  
Author(s):  
Xia Han ◽  
Zhibin Liang ◽  
Caibin Zhang
Keyword(s):  
Risk Model ◽  
Model Parameters ◽  
Proportional Reinsurance ◽  
Surplus Process ◽  
Claim Number ◽  
Common Shock ◽  
Fixed Proportion ◽  
Minimum Probability ◽  
Hamilton Jacobi Bellman ◽  
The Impact

AbstractIn this paper, we study the optimal proportional reinsurance problem in a risk model with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component, and the criterion is to minimise the probability of drawdown, namely, the probability that the value of the surplus process reaches some fixed proportion of its maximum value to date. By the method of maximising the ratio of drift of a diffusion divided to its volatility squared, and the technique of stochastic control theory and the corresponding Hamilton–Jacobi–Bellman equation, we investigate the optimisation problem in two different cases. Furthermore, we constrain the reinsurance proportion in the interval [0,1] for each case, and derive the explicit expressions of the optimal proportional reinsurance strategy and the minimum probability of drawdown. Finally, some numerical examples are presented to show the impact of model parameters on the optimal results.

Hedging of Variable Annuities under Basis Risk

2020 ◽  
Vol 14 (2) ◽  
Author(s):  
Jan Bauer
Keyword(s):  
Financial Market ◽  
Negative Impact ◽  
Mathematical Finance ◽  
Insurance Company ◽  
Hedging Strategy ◽  
Variable Annuities ◽  
Basis Risk ◽  
Hedging Strategies ◽  
Cross Hedging ◽  
Geometric Brownian Motions

AbstractI study dynamic hedging for variable annuities under basis risk. Basis risk, which arises from the imperfect correlation between the underlying fund and the proxy asset used for hedging, has a highly negative impact on the hedging performance. In this paper, I model the financial market based on correlated geometric Brownian motions and analyze the risk management for a pool of stylized GMAB contracts. I investigate whether the choice of a suitable hedging strategy can help to reduce the risk for the insurance company. Comparing several cross-hedging strategies, I observe very similar hedging performances. Particularly, I find that well-established but complex strategies from mathematical finance do not outperform simple and naive approaches in the context studied. Diversification, however, could help to reduce the adverse impact of basis risk.

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