Bayesian optimal investment and reinsurance with dependent financial and insurance risks

Major events like natural catastrophes or the COVID-19 crisis have impact both on the financial market and on claim arrival intensities and claim sizes of insurers. Thus, when optimal investment and reinsurance strategies have to be determined it is important to consider models which reflect this dependence. In this paper we make a proposal how to generate dependence between the financial market and claim sizes in times of crisis and determine via a stochastic control approach an optimal investment and reinsurance strategy which maximizes the expected exponential utility of terminal wealth. Moreover, we also allow that the claim size distribution may be learned in the model. We give comparisons and bounds on the optimal strategy using simple models. What turns out to be very surprising is that numerical results indicate that even a minimal dependence which is created in this model has a huge impact on the control in the sense that the insurer is much more prudent then.Comment: arXiv admin note: text overlap with arXiv:2001.1130

Bayesian optimal investment and reinsurance with dependent financial and insurance risks

Major events like natural catastrophes or the COVID-19 crisis have impact both on the financial market and on claim arrival intensities and claim sizes of insurers. Thus, when optimal investment and reinsurance strategies have to be determined it is important to consider models which reflect this dependence. In this paper we make a proposal how to generate dependence between the financial market and claim sizes in times of crisis and determine via a stochastic control approach an optimal investment and reinsurance strategy which maximizes the expected exponential utility of terminal wealth. Moreover, we also allow that the claim size distribution may be learned in the model. We give comparisons and bounds on the optimal strategy using simple models. What turns out to be very surprising is that numerical results indicate that even a minimal dependence which is created in this model has a huge impact on the control in the sense that the insurer is much more prudent then

Optimal Reinsurance-Investment Strategy for a Monotone Mean-Variance Insurer in the Cram\'er-Lundberg Model

As classical mean-variance preferences have the shortcoming of non-monotonicity, portfolio selection theory based on monotone mean-variance preferences is becoming an important research topic recently. In continuous-time Cram\'er-Lundberg insurance and Black-Scholes financial market model, we solve the optimal reinsurance-investment strategies of insurers under mean-variance preferences and monotone mean-variance preferences by the HJB equation and the HJBI equation, respectively. We prove the validity of verification theorems and find that the optimal strategies under the two preferences are the same. This illustrates that neither the continuity nor the completeness of the market is necessary for the consistency of two optimal strategies. We make detailed explanations for this result. Thus, we develop the existing theory of portfolio selection problems under the monotone mean-variance criterion

Optimal investment and proportional reinsurance in a regime-switching market model under forward preferences

In this paper, we study the optimal investment and reinsurance problem of an insurance company whose investment preferences are described via a forward dynamic exponential utility in a regime-switching market model. Financial and actuarial frameworks are dependent since stock prices and insurance claims vary according to a common factor given by a continuous time finite state Markov chain. We construct the value function and we prove that it is a forward dynamic utility. Then, we characterize the optimal investment strategy and the optimal proportional level of reinsurance. We also perform numerical experiments and provide sensitivity analyses with respect to some model parameters

Optimal investment-reinsurance strategies with state dependent risk aversion and VaR constraints in correlated markets

The final publication is available at Elsevier via https://doi.org/10.1016/j.insmatheco.2018.11.007 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In this paper, we investigate the optimal time-consistent investment–reinsurance strategies for an insurer with state dependent risk aversion and Value-at-Risk (VaR) constraints. The insurer can purchase proportional reinsurance to reduce its insurance risks and invest its wealth in a financial market consisting of one risk-free asset and one risky asset, whose price process follows a geometric Brownian motion. The surplus process of the insurer is approximated by a Brownian motion with drift. The two Brownian motions in the insurer’s surplus process and the risky asset’s price process are correlated, which describe the correlation or dependence between the insurance market and the financial market. We introduce the VaR control levels for the insurer to control its loss in investment–reinsurance strategies, which also represent the requirement of regulators on the insurer’s investment behavior. Under the mean–variance criterion, we formulate the optimal investment–reinsurance problem within a game theoretic framework. By using the technique of stochastic control theory and solving the corresponding extended Hamilton–Jacobi–Bellman (HJB) system of equations, we derive the closed-form expressions of the optimal investment–reinsurance strategies. In addition, we illustrate the optimal investment–reinsurance strategies by numerical examples and discuss the impact of the risk aversion, the correlation between the insurance market and the financial market, and the VaR control levels on the optimal strategies.Natural Science Foundation of China [11571189, 11871219, 11871220]111 Project [B14019]Natural Sciences and Engineering Research Council [RGPIN-2016-03975

Bayesian Optimal Investment and Reinsurance to Maximize Exponential Utility of Terminal Wealth

We herein discuss the surplus process of an insurance company with various lines of business. The claim arrivals of the lines of business are modelled using multivariate point process with interdependencies between the marginal point processes, which depend only on the choice of thinning probabilities. The insurer\u27s aim is to maximize the expected exponential utility of terminal wealth by choosing an investment-reinsurance strategy, in which the insurer can continuously purchase proportional reinsurance and invest its surplus in a Black-Scholes financial market consisting of a risk-free asset and a risky asset. We separately investigate the resulting stochastic control problem under unknown thinning probabilities, unknown claim arrival intensities and unknown claim size distribution for a univariate case. We overcome the issue of uncertainty for these three partial information control problems using Bayesian approaches that result in reduced control problems, for which we characterize the value functions and optimal strategies with the help of the generalized Hamilton-Jacobi-Bellman equation, in which derivatives are replaced by Clarke\u27s generalized gradients. As a result, we could verify that the proposed investment-reinsurance strategy is indeed optimal. Moreover, we analysed the influence of unobservable parameters on optimal reinsurance strategies by deriving comparative results with the case of complete information, which shows a more risk-averse behaviour under more uncertainty. Finally, we provide numerical examples to illustrate the comparison results

The Mathematics and Statistics of Quantitative Risk Management

It was the aim of this workshop to gather a multidisciplinary and international group of scientists at the forefront of research in areas related to the mathematics and statistics of quantitative risk management. The main objectives of this workshop were to break down disciplinary barriers that often limit collaborative research in quantitative risk management, and to communicate the state of the art research from the different disciplines, and to point towards new directions of research