scholarly journals A Penalty Method for the Numerical Solution of Hamilton–Jacobi–Bellman (HJB) Equations in Finance

2011 ◽  
Vol 49 (1) ◽  
pp. 213-231 ◽  
Author(s):  
J. H. Witte ◽  
C. Reisinger
Keyword(s):  
Numerical Solution ◽  
Penalty Method ◽  
Hjb Equations ◽  
Hamilton Jacobi Bellman

scholarly journals A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

2010 ◽  
Author(s):  
J. H. Witte ◽  
C. Reisinger ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Numerical Solution ◽  
Penalty Method ◽  
Hjb Equations ◽  
Hamilton Jacobi Bellman

scholarly journals Policy iteration for Hamilton–Jacobi–Bellman equations with control constraints

2021 ◽  
Author(s):  
Sudeep Kundu ◽  
Karl Kunisch
Keyword(s):  
Linear Equations ◽  
Hjb Equation ◽  
Policy Iteration ◽  
Optimal Feedback Control ◽  
Iteration Step ◽  
Control Constraints ◽  
Hjb Equations ◽  
Bellman Equations ◽  
Hamilton Jacobi Bellman ◽  
Feedback Control Theory

AbstractPolicy iteration is a widely used technique to solve the Hamilton Jacobi Bellman (HJB) equation, which arises from nonlinear optimal feedback control theory. Its convergence analysis has attracted much attention in the unconstrained case. Here we analyze the case with control constraints both for the HJB equations which arise in deterministic and in stochastic control cases. The linear equations in each iteration step are solved by an implicit upwind scheme. Numerical examples are conducted to solve the HJB equation with control constraints and comparisons are shown with the unconstrained cases.

Do Time Preferences Matter in Intertemporal Consumption and Portfolio Decisions?

2019 ◽  
Vol 19 (2) ◽  
Author(s):  
Shou Chen ◽  
Shengpeng Xiang ◽  
Hongbo He
Keyword(s):  
Absolute Risk ◽  
Hyperbolic Discounting ◽  
Time Preferences ◽  
Hjb Equations ◽  
Portfolio Decisions ◽  
Special Cases ◽  
Intertemporal Consumption ◽  
Hamilton Jacobi Bellman ◽  
Hara Utility ◽  
Exponential Discounting

Abstract We study the intertemporal consumption and portfolio rules in the model with the general hyperbolic absolute risk aversion (HARA) utility. The equivalent approximation approach is employed to obtain the Hamilton-Jacobi-Bellman (HJB) equations, and a remarkable property is shown: portfolio rules are independent of the discount function. Moreover, both the consumption and portfolio rates are non-increasing functions of wealth. Particularly illustrative cases examined in detail are the models with the most adopted discount functions, including exponential discounting and hyperbolic discounting. Explicit solutions for intertemporal decisions are found for these special cases, revealing that individual’s time preferences affect the consumption rules only. Moreover, the time-consistent consumption rate under hyperbolic discounting is larger than its counterpart under exponential discounting.

The Meshless Method for Numerical Solution of Modified Equal Width Wave (MEW) Equation

2011 ◽  
Vol 101-102 ◽  
pp. 1130-1133
Author(s):  
Rong Jun Cheng ◽  
Hong Xia Ge
Keyword(s):  
Variational Method ◽  
Numerical Solution ◽  
Meshless Method ◽  
Penalty Method ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Reproducing Kernel Particle Method ◽  
Numerical Examples ◽  
Discrete Equations ◽  
Reproducing Kernel Particle

The reproducing kernel particle method (RKPM) is used in this paper to find the numerical solution of modified equal width wave (MEW) equation. A variational method is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. The effectiveness of the RKPM for the modified equal width equation is investigated by two numerical examples in this paper.

NATURAL GAS-FIRED POWER PLANTS VALUATION AND OPTIMIZATION UNDER LÉVY COPULAS AND REGIME SWITCHING

2017 ◽  
Vol 20 (01) ◽  
pp. 1750004 ◽  
Author(s):  
NEMAT SAFAROV ◽  
COLIN ATKINSON
Keyword(s):  
Natural Gas ◽  
Regime Switching ◽  
Power Plants ◽  
Control Strategies ◽  
Numerical Approach ◽  
Spot Price ◽  
Operating Characteristics ◽  
Hjb Equations ◽  
Explicit Finite Difference ◽  
Hamilton Jacobi Bellman

In this work, we analyze a stochastic control problem for the valuation of a natural gas power station while taking into account operating characteristics. Both electricity and gas spot price processes exhibit mean-reverting spikes and Markov regime-switches. The Lévy regime-switching model incorporates the effects of demand-supply fluctuations in energy markets and abrupt economic disruptions or business cycles. We make use of skewed Lévy copulas to model the dependence risk of electricity and gas jumps. The corresponding coupled Hamilton–Jacobi–Bellman (HJB) equations are solved by an explicit finite difference method. The numerical approach gives us both the value of the plant and its optimal operating strategy depending on the gas and electricity prices, current temperature of the boiler and time. The surfaces of control strategies and contract values are obtained by implementing the numerical method for a particular example.

Optimal Insurance-Package and Investment Problem for an Insurer

2018 ◽  
Vol 6 (1) ◽  
pp. 85-96
Author(s):  
Delei Sheng ◽  
Linfang Xing
Keyword(s):  
Value Function ◽  
Investment Strategy ◽  
Optimal Combination ◽  
Hjb Equations ◽  
Terminal Wealth ◽  
Optimal Insurance ◽  
Yield Rate ◽  
Investment Problem ◽  
Hamilton Jacobi Bellman ◽  
The Value Function

AbstractAn insurance-package is a combination being tie-in at least two different categories of insurances with different underwriting-yield-rate. In this paper, the optimal insurance-package and investment problem is investigated by maximizing the insurer’s exponential utility of terminal wealth to find the optimal combination-share and investment strategy. Using the methods of stochastic analysis and stochastic optimal control, the Hamilton-Jacobi-Bellman (HJB) equations are established, the optimal strategy and the value function are obtained in closed form. By comparing with classical results, it shows that the insurance-package can enhance the utility of terminal wealth, meanwhile, reduce the insurer’s claim risk.

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