scholarly journals Optimal Surrender Policy of Guaranteed Minimum Maturity Benefits in Variable Annuities with Regime-Switching Volatility

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Xiankang Luo ◽  
Jie Xing
Keyword(s):  
Optimal Stopping ◽  
Mutual Fund ◽  
Regime Switching ◽  
Probabilistic Methods ◽  
Optimal Stopping Problem ◽  
American Option Pricing ◽  
Volterra Type ◽  
Variable Annuities ◽  
Type Integral ◽  
Tree Method

This study investigates valuation of guaranteed minimum maturity benefits (GMMB) in variable annuity contract in the case where the guarantees can be surrendered at any time prior to the maturity. In the event of the option being exercised early, early surrender charges will be applied. We model the underlying mutual fund dynamics under regime-switching volatility. The valuation problem can be reduced to an American option pricing problem, which is essentially an optimal stopping problem. Then, we obtain the pricing partial differential equation by a standard Markovian argument. A detailed discussion shows that the solution of the problem involves an optimal surrender boundary. The properties of the optimal surrender boundary are given. The regime-switching Volterra-type integral equation of the optimal surrender boundary is derived by probabilistic methods. Furthermore, a sensitivity analysis is performed for the optimal surrender decision. In the end, we adopt the trinomial tree method to determine the optimal strategy.

scholarly journals Optimal Selling Strategies under Regime-Switching Market Environment with Finite Expiry

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Jie Xing ◽  
Taoshun He
Keyword(s):  
Optimal Stopping ◽  
Regime Switching ◽  
Stock Price ◽  
Stopping Time ◽  
Bear Market ◽  
Type Integral ◽  
Maturity Date ◽  
Finite Time Horizon ◽  
Selling Strategies ◽  
Tree Method

This paper addresses an optimal stock liquidation problem over a finite-time horizon; to that end, we model it as an optimal stopping problem in a regime-switching market. The optimal stopping time is written as a solution to a system of Volterra type integral equations. Moreover, it reveals that when the risk-free interest rate is always lower than the return rate of the stock, it is never optimal to sell the stock early; otherwise, one should sell the stock in bear market if the stock price reaches a critical value and hold the stock in bull market until the maturity date. Finally, we present a trinomial tree method for numerical implementation. The numerical results are consistent with the theoretical findings.

Optimal Retirement Under Partial Information

2021 ◽  
Author(s):  
Kexin Chen ◽  
Junkee Jeon ◽  
Hoi Ying Wong
Keyword(s):  
Optimal Stopping ◽  
Regime Switching ◽  
Bayesian Learning ◽  
Partial Information ◽  
Closed Form Solution ◽  
Form Solution ◽  
Small Scale ◽  
Optimal Stopping Problem ◽  
American Option Pricing ◽  
Potential Applications

The optimal retirement decision is an optimal stopping problem when retirement is irreversible. We investigate the optimal consumption, investment, and retirement decisions when the mean return of a risky asset is unobservable and is estimated by filtering from historical prices. To ensure nonnegativity of the consumption rate and the borrowing constraints on the wealth process of the representative agent, we conduct our analysis using a duality approach. We link the dual problem to American option pricing with stochastic volatility and prove that the duality gap is closed. We then apply our theory to a hidden Markov model for regime-switching mean return with Bayesian learning. We fully characterize the existence and uniqueness of variational inequality in the dual optimal stopping problem, as well as the free boundary of the problem. An asymptotic closed-form solution is derived for optimal retirement timing by small-scale perturbation. We discuss the potential applications of the results to other partial-information settings.

scholarly journals Optimal Selling Rule in a Regime Switching Lévy Market

2011 ◽  
Vol 2011 ◽  
pp. 1-28 ◽  
Author(s):  
Moustapha Pemy
Keyword(s):  
Variational Inequalities ◽  
Viscosity Solution ◽  
Optimal Stopping ◽  
Regime Switching ◽  
Stock Price ◽  
Value Function ◽  
Markov Switching ◽  
Finite Horizon ◽  
Optimal Stopping Problem ◽  
Numerical Example

This paper is concerned with a finite-horizon optimal selling rule problem when the underlying stock price movements are modeled by a Markov switching Lévy process. Assuming that the transaction fee of the selling operation is a function of the underlying stock price, the optimal selling rule can be obtained by solving an optimal stopping problem. The corresponding value function is shown to be the unique viscosity solution to the associated HJB variational inequalities. A numerical example is presented to illustrate the results.

scholarly journals Volterra Type Integral Operators and Composition Operators on Model Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Tesfa Mengestie
Keyword(s):  
Composition Operators ◽  
Integral Operators ◽  
Volterra Type ◽  
Open Problems ◽  
Type Integral ◽  
Model Spaces

We study some mapping properties of Volterra type integral operators and composition operators on model spaces. We also discuss and give out a couple of interesting open problems in model spaces where any possible solution of the problems can be used to study a number of other operator theoretic related problems in the spaces.

scholarly journals On a simple optimal stopping problem

1973 ◽  
Vol 5 (4) ◽  
pp. 297-312 ◽  
Author(s):  
William M. Boyce
Keyword(s):  
Optimal Stopping ◽  
Optimal Stopping Problem

Option Pricing in a Jump-Diffusion Model with Regime Switching

2009 ◽  
Vol 39 (2) ◽  
pp. 515-539 ◽  
Author(s):  
Fei Lung Yuen ◽  
Hailiang Yang
Keyword(s):  
Diffusion Model ◽  
Regime Switching ◽  
Jump Diffusion ◽  
Mathematical Finance ◽  
Extended Model ◽  
Exotic Options ◽  
Switching Model ◽  
Jump Diffusion Model ◽  
Trinomial Tree ◽  
Tree Method

AbstractNowadays, the regime switching model has become a popular model in mathematical finance and actuarial science. The market is not complete when the model has regime switching. Thus, pricing the regime switching risk is an important issue. In Naik (1993), a jump diffusion model with two regimes is studied. In this paper, we extend the model of Naik (1993) to a multi-regime case. We present a trinomial tree method to price options in the extended model. Our results show that the trinomial tree method in this paper is an effective method; it is very fast and easy to implement. Compared with the existing methodologies, the proposed method has an obvious advantage when one needs to price exotic options and the number of regime states is large. Various numerical examples are presented to illustrate the ideas and methodologies.

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