Search

We present a streamlined valuation method for the guaranteed minimum accumulation benefits incorporated within variable annuity contracts. At each contract renewal date, the insurer updates the policyholder's account value to the higher of the guaranteed value and the equity-linked investment value. In addition, we introduce lapse risks into the variable annuity contract, modeling the lapse decision under the assumption of stochastic intensity. Utilizing a combination of continuous-time Markov chain approximation and the Fourier cosine series expansion method, we derive closed-form valuation formulas under regime switching jump diffusion models. Numerical simulations showcase the precision and effectiveness of the proposed approach. • This paper proposes an efficient computational method for pricing variable annuities. • Our results significantly improve computational efficiency compared to Monte Carlo. • We introduce lapse risk and regime-switching into the paper. • Our method can be used to calculate option pricing. [ABSTRACT FROM AUTHOR]

• A Cox risk model with periodic capital injections and dividend payments is used to model the insurance company surplus level. • The stochastic intensity process is represented by a general stochastic differential equation. • The insurer discrete observes the level of surplus and makes capital injections, dividend payments, and ruin decisions based on the observed level of surplus. • The continuous time Markov chain technique is combined with the Fourier cosine series expansion method to compute the finite-time expected present value of operating costs until ruin. • The optimal critical levels of capital injections and dividend payments are investigated, as well as the impact of some parameters on the results. In this paper, we use a Cox risk model to describe the surplus flow of an insurance company, where the intensity process in the Cox process is assumed to follow a general stochastic differential equation. Suppose that the insurer observes the surplus process periodically with constant observation frequency. Whenever the observed surplus level is larger than a critical level b 2 > 0 , the excess amount is paid as a lump sum of dividends; whenever the observed surplus level is between zero and another critical level b 1 (0 < b 1 < b 2), capital is injected to the surplus process so that it return to the level b 1 ; whenever the observed surplus level is less than zero, ruin is declared and the process is stopped. Under these assumptions, we study the finite-time expected present value of operating costs until ruin. The continuous time Markov chain (CTMC) approximation technique is used to approximate the intensity process in the Cox model, and the Fourier cosine series expansion (COS) method is applied to approximate the function of interest. A lot of numerical results are given to show accuracy and efficiency of our method, and impacts of some parameters are also analyzed. [ABSTRACT FROM AUTHOR]

In this paper, we consider a compound Poisson model under a mixed dividend strategy. The mixed dividend strategy is a combination of threshold dividend strategy and periodic dividend strategy. Given a positive threshold level b  > 0, whenever the surplus process attains the level b , dividends will be paid off continuously at a rate α  > 0. Furthermore, given a sequence of dividend decision times { Z j } j = 1 ∞ , whenever the observed surplus level at Z j is larger than b , the excess value will also be paid off as dividend. We study the expected discounted dividend payments before ruin and the Gerber–Shiu expected discounted penalty function. Some numerical examples are also presented. [ABSTRACT FROM AUTHOR]

• We consider the pricing problem for GMDB products under general regime - switching jump diffusion models. • The complex Fourier series expansion method is applied to approximate the pricing formulas. • A lot of numerical examples are provided to show effectiveness of our pricing method. In this paper, we consider the valuation problem of equity-linked annuity with guaranteed minimum death benefit (GMDB) by complex Fourier series method under regime-switching jump diffusion models. We show that the price formulas can be expressed by some discounted density functions associated with the residual lifetime random variable. Fourier transforms for discounted density functions are derived, and complex Fourier series expansion method is applied to recover the discounted density functions. Some explicit formulas for computing the GMDB price are given. Finally, we give some numerical results to show effectiveness of our method. [ABSTRACT FROM AUTHOR]

• We consider the finite time dividend-ruin problems with constant inter-observation times. • Recursive methods for computing the finite time expected discounted penalty function and the present value of dividend payments are proposed. • Error analysis are made for our algorithm. • Numerical results are provided to show effectiveness of our method. In this paper, we use a Lévy process to model the surplus flow of an insurance company. It is assumed that the surplus level is observed at a sequence of fixed times and dividend decisions are made at each observation time. If the observed surplus level is larger than a given barrier, then the excess amount would be paid off as a lump sum of dividends. Further, we assume that ruin is declared as soon as the observed surplus level is negative. Using the Fourier cosine series expansion method, we propose some numerical methods for computing the finite-time expected discounted dividend payments before ruin and the finite-time expected discounted penalty function. Both error analysis and numerical examples are given to show accuracy and efficiency of our method. [ABSTRACT FROM AUTHOR]

• We propose a general theoretical framework for systematically deriving explicit closed-form expressions of the first passage time density functions in a class of jump diffusion processes with phase-type jumps. • Our method is based on the projection idea in L2 space and theory of the Laguerre series. • Two methods for deriving the Laguerre coefficients are proposed. • A lot of numerical examples are given to show the effectiveness of the proposed method. We propose for the first time some explicit closed-form Laguerre series expansion formulas for the first passage time density functions of a jump diffusion model. Suppose that the jumps in the model are phase-type distributed. In contrast to existing methods in the literature based on numerical Laplace transform inversion, the proposed formulas are in analytical closed-form and simple to implement. Two different methods are proposed to compute the Laguerre coefficients. Various numerical examples are also given to show the effectiveness of our method. [ABSTRACT FROM AUTHOR]