scholarly journals Explicit Solution of Reinsurance-Investment Problem for an Insurer with Dynamic Income under Vasicek Model

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
De-Lei Sheng
Keyword(s):  
Explicit Solution ◽  
Bellman Equation ◽  
Control Technique ◽  
Power Utility ◽  
Terminal Wealth ◽  
Investment Problem ◽  
Stochastic Interest ◽  
Hamilton Jacobi Bellman Equation ◽  
Interest Rate Model ◽  
Hamilton Jacobi Bellman

Unlike traditionally used reserves models, this paper focuses on a reserve process with dynamic income to study the reinsurance-investment problem for an insurer under Vasicek stochastic interest rate model. The insurer’s dynamic income is given by the remainder after a dynamic reward budget being subtracted from the insurer’s net premium which is calculated according to expected premium principle. Applying stochastic control technique, a Hamilton-Jacobi-Bellman equation is established and the explicit solution is obtained under the objective of maximizing the insurer’s power utility of terminal wealth. Some economic interpretations of the obtained results are explained in detail. In addition, numerical analysis and several graphics are given to illustrate our results more meticulous.

scholarly journals The Optimal Strategy of Reinsurance-Investment Problem for an Insurer with Dynamic Income Under Stochastic Interest Rate

2016 ◽  
Vol 4 (3) ◽  
pp. 244-257
Author(s):  
Delei Sheng
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Control Technique ◽  
Stochastic Interest Rate ◽  
Insurance Company ◽  
Power Utility ◽  
Investment Problem ◽  
Stochastic Interest ◽  
Hamilton Jacobi Bellman ◽  
Constant Interest Rate

AbstractThis paper considers the reinsurance-investment problem for an insurer with dynamic income to balance the profit of insurance company and policy-holders. The insurer’s dynamic income is given by a net premium minus a dynamic reward budget item and the net premium is obtained according to the expected premium principle. Applying the stochastic control technique, a Hamilton-Jacobi-Bellman equation is established under stochastic interest rate model and the explicit solution is obtained by maximizing the insurer’s power utility of terminal wealth. In addition, the comparison with corresponding results under constant interest rate helps us to understand the role and influence of stochastic interest rates more in-depth.

scholarly journals Optimal Expected Utility of Dividend Payments with Proportional Reinsurance under VaR Constraints and Stochastic Interest Rate

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yuzhen Wen ◽  
Chuancun Yin
Keyword(s):  
Optimal Strategy ◽  
Bellman Equation ◽  
Insurance Company ◽  
Time Value ◽  
Dividend Payments ◽  
Discounted Utility ◽  
Stochastic Interest ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman ◽  
The Value Function

In this paper, we consider the problem of maximizing the expected discounted utility of dividend payments for an insurance company taking into account the time value of ruin. We assume the preference of the insurer is of the CRRA form. The discounting factor is modeled as a geometric Brownian motion. We introduce the VaR control levels for the insurer to control its loss in reinsurance strategies. By solving the corresponding Hamilton-Jacobi-Bellman equation, we obtain the value function and the corresponding optimal strategy. Finally, we provide some numerical examples to illustrate the results and analyze the VaR control levels on the optimal strategy.

Interception of automated adversarial drone swarms in partially observed environments

2021 ◽  
pp. 1-14
Author(s):  
Daniel Saranovic ◽  
Martin Pavlovski ◽  
William Power ◽  
Ivan Stojkovic ◽  
Zoran Obradovic
Keyword(s):  
Bellman Equation ◽  
Pid Controllers ◽  
Partially Observed ◽  
Hamilton Jacobi Bellman Equation ◽  
Partial Feedback ◽  
Point Solution ◽  
Physical Limitations ◽  
Defensive Mechanisms ◽  
Hamilton Jacobi Bellman ◽  
New Framework

As the prevalence of drones increases, understanding and preparing for possible adversarial uses of drones and drone swarms is of paramount importance. Correspondingly, developing defensive mechanisms in which swarms can be used to protect against adversarial Unmanned Aerial Vehicles (UAVs) is a problem that requires further attention. Prior work on intercepting UAVs relies mostly on utilizing additional sensors or uses the Hamilton-Jacobi-Bellman equation, for which strong conditions need to be met to guarantee the existence of a saddle-point solution. To that end, this work proposes a novel interception method that utilizes the swarm’s onboard PID controllers for setting the drones’ states during interception. The drone’s states are constrained only by their physical limitations, and only partial feedback of the adversarial drone’s positions is assumed. The new framework is evaluated in a virtual environment under different environmental and model settings, using random simulations of more than 165,000 swarm flights. For certain environmental settings, our results indicate that the interception performance of larger swarms under partial observation is comparable to that of a one-drone swarm under full observation of the adversarial drone.

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