Optimal investment strategy for annuity contracts under the constant elasticity of variance (CEV) model

This paper focuses on the constant elasticity of variance (CEV) model for studying the optimal investment strategy before and after retirement in a defined contribution pension plan where benefits are paid under the form of annuities; annuities are supposed to be guaranteed during a certain fixed period of time. Using Legendre transform, dual theory and variable change technique, we derive the explicit solutions for the power and exponential utility functions in two different periods (before and after retirement). Each solution contains a modified factor which reflects an investor’s decision to hedge the volatility risk. In order to investigate the influence of the modified factor on the optimal strategy, we analyze the property of the modified factor. The results show that the dynamic behavior of the modified factor for the power utility mainly depends on the time and the investor’s risk aversion coefficient, whereas it only depends on the time in the exponential case.     

Pooling,pricing and trading of risks

Exchange of risks is considered here as a transferable-utility, cooperative game, featuring risk averse players. Like in competitive equilibrium, a core solution is determined by shadow prices on state-dependent claims. And like in finance, no risk can properly be priced merely in terms of its marginal distribution. Pricing rather depends on the pooled risk and on the convolution of individual preferences. The paper elaborates on these features, placing emphasis on the role of prices and incompleteness. Some novelties come by bringing questions about existence, computation and uniqueness of solutions to revolve around standard Lagrangian duality. Especially outlined is how repeated bilateral trade may bring about a price-supported core allocation.     

Low-order self-tuner for fault-tolerant control of a class of unknown nonlinear stochastic sampled-data systems

Based on the modified state-space self-tuning control (STC) via the observer/Kalman filter identification (OKID) method, an effective low-order tuner for fault-tolerant control of a class of unknown nonlinear stochastic sampled-data systems is proposed in this paper. The OKID method is a time-domain technique that identifies a discrete input–output map by using known input–output sampled data in the general coordinate form, through an extension of the eigensystem realization algorithm (ERA). Then, the above identified model in a general coordinate form is transformed to an observer form to provide a computationally effective initialization for a low-order on-line “auto-regressive moving average process with exogenous (ARMAX) model”-based identification. Furthermore, the proposed approach uses a modified Kalman filter estimate algorithm and the current-output-based observer to repair the drawback of the system multiple failures. Thus, the fault-tolerant control (FTC) performance can be significantly improved. As a result, a low-order state-space self-tuning control (STC) is constructed. Finally, the method is applied for a three-tank system with various faults to demonstrate the effectiveness of the proposed methodology.     

Coordinating a supply chain with effort and price dependent stochastic demand

This paper investigates the issue of channel coordination for a supply chain facing stochastic demand that is sensitive to both sales effort and retail price. In the standard newsvendor setting, the returns policy and the revenue sharing contract have been shown to be able to align incentives of the supply chain’s members so that the decentralized supply chain behaves as well as the integrated one. When the demand is influenced by both retail price and retailer sales effort, none of the above traditional contracts can coordinate the supply chain. To resolve this issue, we explore a variety of other contract types including joint return policy with revenue sharing contract, return policy with sales rebate and penalty (SRP) contract, and revenue sharing contract with SRP. We find that only the properly designed returns policy with SRP contract is able to achieve channel coordination and lead to a Pareto improving win–win situation for supply chain members. We then provide analytical method to determine the contract parameters and finally we use a numerical example to illustrate the findings and gain more insights.     

On multistage Stochastic Integer Programming for incorporating logical constraints in asset and liability management under uncertainty

We present a model for optimizing a mean-risk function of the terminal wealth for a fixed income asset portfolio restructuring with uncertainty in the interest rate path and the liabilities along a given time horizon. Some logical constraints are considered to be satisfied by the assets portfolio. Uncertainty is represented by a scenario tree and is dealt with by a multistage stochastic mixed 0-1 model with complete recourse. The problem is modelled as a splitting variable representation of the Deterministic Equivalent Model for the stochastic model, where the 0-1 variables and the continuous variables appear at any stage. A Branch-and-Fix Coordination approach for the multistage 0–1 program solving is proposed. Some computational experience is reported.      

A branch-and-cut algorithm for the stochastic uncapacitated lot-sizing problem

This paper addresses a multi-stage stochastic integer programming formulation of the uncapacitated lot-sizing problem under uncertainty. We show that the classical (ℓ,S) inequalities for the deterministic lot-sizing polytope are also valid for the stochastic lot-sizing polytope. We then extend the (ℓ,S) inequalities to a general class of valid inequalities, called the inequalities, and we establish necessary and sufficient conditions which guarantee that the inequalities are facet-defining. A separation heuristic for inequalities is developed and incorporated into a branch-and-cut algorithm. A computational study verifies the usefulness of the inequalities as cuts. This research has been supported in part by the National Science Foundation under Award number DMII-0121495.     

Dynamics of a stochastic Lotka-Volterra model perturbed by white noise

This paper continues the study of Mao et al. investigating two aspects of the equation

     

Expected present value of total dividends in a delayed claims risk model under stochastic interest rates

In this paper, a compound binomial risk model with a constant dividend barrier under stochastic interest rates is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. In the evaluation of the expected present value of dividends, the interest rates are assumed to follow a Markov chain with finite state space. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are K_n distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends.     

Mathematical foundation of nonequilibrium fluctuation–dissipation theorems for inhomogeneous diffusion processes with unbounded coefficients

Nonequilibrium fluctuation–dissipation theorems (FDTs) are one of the most important advances in stochastic thermodynamics over the past two decades. Here we provide rigorous mathematical proofs of two types of nonequilibrium FDTs for inhomogeneous diffusion processes with unbounded drift and diffusion coefficients by using the Schauder estimates for partial differential equations of parabolic type and the theory of weakly continuous semigroups. The FDTs proved in this paper apply to any forms of inhomogeneous and nonlinear external perturbations. Furthermore, we prove the uniqueness of the conjugate observables and clarify the precise mathematical conditions and ranges of applicability for the two types of FDTs. Examples are also given to illustrate the main results of this paper.     

Concentration inequalities for stochastic differential equations of pure non-Poissonian jumps

We provide concentration inequalities for solutions to stochastic differential equations of pure not-necessarily Poissonian jumps. Our proofs are based on transportation cost inequalities for square integrable functionals of point processes with stochastic intensity and elements of stochastic calculus with respect to semi-martingales. We apply the general results to solutions of stochastic differential equations driven by renewal and non-linear Hawkes point processes.