scholarly journals On the Bellman equation for asymptotics of utility from terminal wealth

2010 ◽  
Vol 37 (1) ◽  
pp. 89-97
Author(s):  
Janusz Matkowski ◽  
Łukasz Stettner
Keyword(s):  
Bellman Equation ◽  
Terminal Wealth

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.

OPTIMAL INVESTMENT DECISIONS FOR A PORTFOLIO WITH A ROLLING HORIZON BOND AND A DISCOUNT BOND

2005 ◽  
Vol 08 (07) ◽  
pp. 871-913 ◽  
Author(s):  
TOMASZ R. BIELECKI ◽  
STANLEY PLISKA ◽  
JIONGMIN YONG
Keyword(s):  
Bellman Equation ◽  
Planning Horizon ◽  
Optimal Investment ◽  
Economic Factors ◽  
Rolling Horizon ◽  
Bank Account ◽  
Terminal Wealth ◽  
Riskless Asset ◽  
Optimal Investment Problem ◽  
First Time

An optimal investment problem is considered for a continuous-time market consisting of the usual bank account, a rolling horizon bond, and a discount bond whose maturity coincides with the planning horizon. Two economic factors, namely, the short rate and the risk-free yield of some fixed maturity, are modeled as Gaussian processes. For the problem of maximizing expected CRRA utility of terminal wealth, the optimal portfolio is obtained through a Bellman equation. The results are noteworthy because the discount bond, which is the riskless asset for the investor, causes a degeneracy due to its zero volatility at the planning horizon. Indeed, this delicate matter is treated rigorously for what seems to be the first time, and it is shown that there exists an optimal, admissible (but unbounded) trading strategy.

Cost averaging: An expensive strategy for maximising terminal wealth

2003 ◽  
Vol 17 (2) ◽  
pp. 186-193 ◽  
Author(s):  
Bernd Scherer ◽  
Thomas Ebertz
Keyword(s):  
Terminal Wealth

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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