Pension funding incorporating downside risks

Chang, Shih-Chieh; Tzeng, Larry Y.; Miao, Jerry C.Y.

doi:10.1016/s0167-6687(02)00211-1

Cited by 35 publications

(28 citation statements)

References 23 publications

(44 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…On the other hand, the second term F (0) is just the initial reserve to operate the scheme. There is much literature to study the stochastic optimization of pension funds, such as Chang, Tzeng, and Miao [3], Owadally and Haberman [11], Ngwira and Gerrard [10], etc. However, our problems are essentially different in that we study the optimal pension fund problem in the framework of LQ backward controls.…”

Section: Dδ(t) = [R(t) + (μ(T) − R(t))π(t)]dt + σ(T)π(t)dw (T)mentioning

confidence: 99%

A Maximum Principle for Partial Information Backward Stochastic Control Problems with Applications

Huang¹,

Wang²,

Xiong³

2009

SIAM J. Control Optim.

View full text Add to dashboard Cite

Abstract. This paper studies the partial information control problems of backward stochastic systems. There are three major contributions made in this paper: (i) First, we obtain a new stochastic maximum principle for partial information control problems. Our method relies on a direct calculation of the derivative of the cost functional. (ii) Second, we introduce two classes of partial information linear-quadratic backward control problems for the first time and then investigate them using the maximum principle. Complete and explicit solutions are obtained in terms of some forward and backward stochastic differential filtering equations. (iii) Last but not least, we study a class of full information stochastic pension fund optimization problems which can be viewed as a special case of our general partial information ones. Applying the aforementioned maximum principle, we derive the optimal contribution policy in closed-form and present some related economic remarks. ). In particular, the celebrated Black-Scholes option pricing formula can be derived from a class of linear BSDEs, where the random terminal condition is just the option's payoff at the maturity.Since BSDEs are well-defined dynamic systems, it is very natural and appealing to consider the control problems of BSDEs. However, there exist only a few works along this line, including Peng [13], Xu [22], Wu [19], Lim and Zhou [7], and Wang and Yu [17]. Our work distinguishes itself from the above ones in the following aspects: (i) Our work is established in the context of partial information which is rather general than that of the partial observation. In fact, our information can be summarized by any subfiltration and free of specific observation structures; thus it includes the partial observation models (in particular, the white noise observation models) as its special cases (see, e.g., Wu [20], Wang and Wu [15]). (ii) Two important classes of partial

show abstract

Section: Dδ(t) = [R(t) + (μ(T) − R(t))π(t)]dt + σ(T)π(t)dw (T)mentioning

confidence: 99%

A Maximum Principle for Partial Information Backward Stochastic Control Problems with Applications

Huang¹,

Wang²,

Xiong³

2009

SIAM J. Control Optim.

View full text Add to dashboard Cite

show abstract

“…Note that the specification (5) implies that the fund manager assigns the same importance to over and under deviations of the fund's assets and contributions from their respective targets. The recent paper by Chang et al (2003) considers the square of ratio deviation of the variables, plus linear terms in the performance criterion function, in such a way that under-funding and over-contributing is more penalized than over-funding and under-contributing.…”

Section: Optimal Funding With Safe Investmentmentioning

confidence: 99%

Optimal risk management in defined benefit stochastic pension funds

Josa-Fombellida

Rincón‐Zapatero

2004

Insurance: Mathematics and Economics

View full text Add to dashboard Cite

We consider a continuous time dynamic pension funding model in a defined benefit plan of an employment system. The benefits liabilities are random, given by a geometric Brownian process. Three different situations are studied regarding the investment decisions taken by the sponsoring employer: in the first, the fund is invested at a constant, risk-free rate of interest; in the second, the promoter invests in a portfolio with n risky assets and a risk-free security; finally, it is supposed that the rate of return is stochastic. Modelling the preferences of the manager such that the main objective is to minimize both the contribution rate risk and the solvency risk, we study cases where the optimal behavior leads to a spread method of funding. JEL classification: G23; G11Subj. classification: E13; B81

show abstract

“…There are a lot of papers dealing with defined benefit pension plans, see for example Haberman, Sung (1994), Haberman et al (2000), Cairns (2000), Chang et al (2003), Haberman, Sung (2005). However, we are aware of only two in which a pension liability is a random variable.…”

Section: Introductionmentioning

confidence: 99%

Mean–variance optimization problems for an accumulation phase in a defined benefit plan

Delong

Gerrard²,

Haberman³

2008

Insurance: Mathematics and Economics

View full text Add to dashboard Cite

In this paper we deal with contribution rate and asset allocation strategies in a pre-retirement accumulation phase. We consider a single cohort of workers and investigate a retirement plan of a defined benefit type in which an accumulated fund is converted into a life annuity. Due to the random evolution of a mortality intensity, the future price of an annuity, and as a result, the liability of the fund, is uncertain. A manager has control over a contribution rate and an investment strategy and is concerned with covering the random claim. We consider two mean-variance optimization problems, which are quadratic control problems with an additional constrain on the expected value of the terminal surplus of the fund. This functional objectives can be related to the well-established financial theory of claim hedging. The financial market consists of a risk-free asset with a constant force of interest and a risky asset which price is driven by a Lévy noise, whereas the evolution of a mortality intensity is described by a stochastic differential equation driven by a Brownian motion. Techniques from the stochastic control theory are applied in order to find optimal strategies.

show abstract

Pension funding incorporating downside risks

Cited by 35 publications

References 23 publications

A Maximum Principle for Partial Information Backward Stochastic Control Problems with Applications

A Maximum Principle for Partial Information Backward Stochastic Control Problems with Applications

Optimal risk management in defined benefit stochastic pension funds

Mean–variance optimization problems for an accumulation phase in a defined benefit plan

Contact Info

Product

Resources

About