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Showing 1 to 12 of 12 for “"Hamilton-Jacobi-Bellman equation"”.
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Hamilton-Jacobi-Bellman equation for stochastic optimal control: Applications to spacecraft attitude control
… dynamics is derived through formulation of the Hamilton-Jacobi-Bellman equation associated with a stochastic differential equation. The solution to the Hamilton-Jacobi-Bellman partial differential equation is approximated through the method of Al’brekht [1]. Extension of Albrekht method for a …
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Superreplication method for multi-asset barrier options.
… using rather standard arguments we derive the Hamilton-Jacobi-Bellman equation for the value function. We show that the value function is a unique viscosity solution of the Hamilton-Jacobi-Bellman equation. Then we define the super price and superhedging strategy for the barrier options and …
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Reinsurance and dividend management
… the resulting second-order partial differential equation known as Hamilton-Jacobi-Bellman equation. We find out that the optimal retention level is linear with the current reserve up to a point whereupon it is optimal for the insurance company to retain all business. As for the optimal dividend …
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Stochastic Control, Optimal Saving, and Job Search in Continuous Time
… each obey a specific stochastic differential equation, where uncertainty stems either from Poisson or Lévy processes. The results on the optimal behavior are derived by maximizing the individual expected lifetime utility. The first chapter is concerned with the necessary mathematical tools, …
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Optimal choices: mean field games with controlled jumps and optimality in a stochastic volatility model
… in the control itself. The solvability of the Hamilton-Jacobi-Bellman equation associated to this optimal control problem is discussed.
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A State Space Partitioning Scheme for Vehicle Control in Pursuit-Evasion Scenarios
… are incorporated into the control by solving the Hamilton-Jacobi-Isaacs (HJI) equation explicitly, simplifying the solution using approximate dynamic programming, or using a purely finite-horizon approach. Unfortunately, these methods are either subject to difficulties of long computational times …
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A generalized label correcting method for optimal kinodynamic motion planning
… are used to derive a generalization of Bellman's principle of optimality in the context of kinodynamic motion planning. A generalized label correcting algorithm is then proposed which leverages these results to prune candidate input signals from the search when their cost is greater than …
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Modelling of asset allocation in banking using the mean-variance approach
… which are the so called martingale method and Hamilton Jacobi Bellman method. We shall follow the latter. As is common in portfolio op- timization problems, we obtain an explicit solution for the value function in the Hamilton Jacobi Bellman equation. Our approach to the portfolio prob- lem is …
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Retirement Annuities: Optimization, Analysis and Machine Learning
… optimal control problem, solve its centerpiece Hamilton-Jacobi-Bellman equation numerically, and provide a verification theorem. The result is an optimal DIA purchasing map. With Cash Refund Income Annuities (CRIA) gaining traction quickly over the past few years, the literature is growing in …
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Topics in Trajectory Generation for Robots
… as a controller design problem. Using the Hamilton-Jacobi-Bellman equation, we derive a closed-loop solution to the fixed-time trajectory-generation problem with a minimum-jerk cost functional. We show that the resulting trajectory coincides with a fifth-order polynomial function of time …
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The Importance of the Riemann-Hilbert Problem to Solve a Class of Optimal Control Problems
Optimal control problems can in many cases become complicated and difficult to solve. One particular class of difficult control problems to solve are singular control problems. Standard methods for solving optimal control are discussed showing why those methods are difficult to apply to singular …