Journal ArticleDOI
Convergence of numerical schemes for parabolic equations arising in finance theory
G. Barles,Ch. Daher,M. Romano +2 more
TLDR
This paper is essentially expository but it presents however new results concerning some problems of rate of convergence in Finance theory.Abstract:
We present several results and methods concerning the convergence of numerical schemes for problems arising in Finance theory. This paper is essentially expository but we present however new results concerning some problems of rate of convergence.read more
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Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE
TL;DR: In this paper, the authors propose a method for solving control problems by verification, which is based on the Viscosity Solution Equation (VSP) in the sense of VVS.
Journal ArticleDOI
A bibliography on moving-free boundary problems for the heat-diffusion equation. The stefan and related problems
TL;DR: Tarzia et al. as discussed by the authors presented a bibliografía on moving and free boundary problems for the heatdiffusion equation, particularly regarding the Stefan and related problems, which contains 5869 titles referring to 588 scientific journals, 122 books, 88 symposia, 30 collections, 59 thesis and 247 technical reports.
Journal ArticleDOI
Numerical methods for controlled Hamilton-Jacobi-Bellman PDEs in finance
Peter Forsyth,George Labahn +1 more
TL;DR: In this paper, the authors show that the nonlinear option pricing problem can be formulated as an optimal control problem, leading to Hamilton-Jacobi-Bellman (HJB) or HJBI (HJBI-Isaacs) equations, which are very convenient for developing monotone discretization methods which ensure convergence to the financially relevant solution.
MonographDOI
Splitting methods for partial differential equations with rough solutions : analysis and MATLAB programs
Journal ArticleDOI
Guaranteed Minimum Withdrawal Benefit in Variable Annuities
Abstract: We develop a singular stochastic control model for pricing variable annuities with the guaranteed minimum withdrawal benefit. This benefit promises to return the entire initial investment, with withdrawals spread over the term of the contract, irrespective of the market performance of the underlying asset portfolio. A contractual withdrawal rate is set and no penalty is imposed when the policyholder chooses to withdraw at or below this rate. Subject to a penalty fee, the policyholder is allowed to withdraw at a rate higher than the contractual withdrawal rate or surrender the policy instantaneously. We explore the optimal withdrawal strategy adopted by the rational policyholder that maximizes the expected discounted value of the cash flows generated from holding this variable annuity policy. An effcient finite difference algorithm using the penalty approximation approach is proposed for solving the singular stochastic control model. Optimal withdrawal policies of the holders of the variable annuities with the guaranteed minimum withdrawal benefit are explored. We also construct discrete pricing formulation that models withdrawals on discrete dates. Our numerical tests show that the solution values from the discrete model converge to those of the continuous model.