A maximum principle for optimal control problem of fully coupled forward-backward stochastic systems with partial information

The paper is concerned with a stochastic optimal control problem in which the controlled system is described by a fully coupled nonlinear forward-backward stochastic differential equation driven by a Brownian motion.It is required that all admissible control processes are adapted to a given subfiltration of the filtration generated by the underlying Brownian motion.For this type of partial information control,one sufficient(a verification theorem) and one necessary conditions of optimality are proved.The control domain need to be convex and the forward diffusion coefficient of the system can contain the control variable.

Probabilistic inference of fatigue damage propagation with limited and partial information

A general method of probabilistic fatigue damage prognostics using limited and partial information is developed.Limited and partial information refers to measurable data that are not enough or cannot directly be used to statistically identify model parameter using traditional regression analysis.In the proposed method, the prior probability distribution of model parameters is derived based on the principle of maximum entropy（Max Ent） using the limited and partial information as constraints.The posterior distribution is formulated using the principle of maximum relative entropy（MRE） to perform probability updating when new information is available and reduces uncertainty in prognosis results.It is shown that the posterior distribution is equivalent to a Bayesian posterior when the new information used for updating is point measurements.A numerical quadrature interpolating method is used to calculate the asymptotic approximation for the prior distribution.Once the prior is obtained, subsequent measurement data are used to perform updating using Markov chain Monte Carlo（MCMC） simulations.Fatigue crack prognosis problems with experimental data are presented for demonstration and validation.

On Optimal Mean-Field Control Problem of Mean-Field Forward-Backward Stochastic System with Jumps Under Partial Information

This paper considers the problem of partially observed optimal control for forward-backward stochastic systems driven by Brownian motions and an independent Poisson random measure with a feature that the cost functional is of mean-field type. When the coefficients of the system and the objective performance functionals are allowed to be random, possibly non-Markovian, Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed. The authors also investigate the mean-field type optimal control problem for the system driven by mean-field type forward-backward stochastic differential equations(FBSDEs in short) with jumps, where the coefficients contain not only the state process but also its expectation under partially observed information. The maximum principle is established using convex variational technique. An example is given to illustrate the obtained results.

Optimal Reinsurance and Investment Strategies Under Mean-Variance Criteria:Partial and Full Information

This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be directly observed. And the short-selling of stocks is prohibited. The problem is formulated as a stochastic linear-quadratic control problem where the control variables are constrained. Based on the separation principle and stochastic filtering theory, the partial information problem is solved. Efficient strategies and efficient frontier are presented in closed forms via solutions to two extended stochastic Riccati equations. As a comparison, the efficient strategies and efficient frontier are given by the viscosity solution to the HJB equation in the full information case. Some numerical illustrations are also provided.

A Complex Algorithm for Solving a Kind of Stochastic Programming

Considering that the probability distribution of random variables in stochastic programming usually has incomplete information due to a perfect sample data in many real applications, this paper discusses a class of two-stage stochastic programming problems modeling with maximum minimum expectation compensation criterion (MaxEMin) under the probability distribution having linear partial information (LPI). In view of the nondifferentiability of this kind of stochastic programming modeling, an improved complex algorithm is designed and analyzed. This algorithm can effectively solve the nondifferentiable stochastic programming problem under LPI through the variable polyhedron iteration. The calculation and discussion of numerical examples show the effectiveness of the proposed algorithm.

Optimal power and subcarrier allocation with partial side information for downlink OFDMA system

In this paper,we investigate the power and subcarrier allocation issue in the case of partial side information for downlink orthogonal frequency division multiple access （OFDMA） system.Relaxation method is utilized to characterize the necessary conditions of the optimal solution and the uniqueness of the optimal solution is proved.The game theoretical concept,surplus function is also introduced to analyze the optimal solution.Based on the theoretical analysis,we propose iterative surplus balancing algorithm （ISBA） that can jointly assign the power and subcarriers in multiple rounds,and then the optimality of ISBA is proved.Simulation results are presented to show the characteristics of the theoretical analysis and ISBA.

Partially Observed Risk-Sensitive Stochastic Control Problems with Non-Convexity Restriction

The paper considers partially observed optimal control problems for risk-sensitive stochastic systems,where the control domain is non-convex and the diffusion term contains the control v.Utilizing Girsanov’s theorem,spike variational technique as well as duality method,the authors obtain four adjoint equations and establish a maximum principle under partial information.As an application,an example is presented to demonstrate the result.

HOW DOES THE RETAILER MAKE PRICING DECISION WHEN CONSUMERS HAVE JUSTICE REFERENCE PRICE

A series of studies demonstrate that consumers have fairness judgments about the retailer＇s price which will impact their shopping decisions. Thus, it is necessary for the retailer to take consumers＇ fairness concerns into account when setting his pricing policies. We assume that when the retailer＇s price is lower than a consumer＇s justice reference price, the consumer is likely to sense a positive price unfairness that will lead to increased consumer utility, and when the retailer＇s price is higher than a consumer＇s justice reference price, the consumer is likely to sense a negative price unfairness-that will have a negative effect on consumer utility. According to the information conditions of the consumers＇ justice reference price, the retailer should consider three situations： certain information, random information and partial information. In all situations, we show that the retailer has a unique optimal pricing strategy. Finally, through numerical examples, we find that our distribution-free policies perform almost the same as the results under the distributions that maximize the entropy. Our results reveal that it is important for the retailer to consider consumers＇ fairness concerns, otherwise he may suffer losses when Pc is very small.

CLAIM HEDGING IN AN INCOMPLETE MARKET

In this paper, we compare the performance of the optimal attainable payoffs (of a general claim) derived by the variance-optimal approach and the indifference argument under the mean-variance preference in an incomplete market. Both payoffs are expressed by the signed variance-optimal martingale measure. Our results are applied to the claim hedging under partial information.

Optimal Two-Part Tariff Licensing in a Differentiated Mixed Duopoly

This paper considers the two-part tariff licensing by an innovating firm to its potential competitor in a differentiated mixed duopoly, in which one firm sets a quantity and the other firm charges a price. Based on the development cost incurred by the rival, we derive the optimal behavior of the firms under full information case and partial information case respectively. Information difference on the equilibrium strategies is also investigated.

AN EXTENDED BLOCK RESTRICTED ISOMETRY PROPERTY FOR SPARSE RECOVERY WITH NON-GAUSSIAN NOISE

We study the recovery conditions of weighted mixedl2/lp minimization for block sparse signal reconstruction from compressed measurements when partial block support information is available.We show theoretically that the extended block restricted isometry property can ensure robust recovery when the data fidelity constraint is expressed in terms of anlq norm of the residual error,thus establishing a setting wherein we are not restricted to Gaussian measurement noise.We illustrate the results with a series of numerical experiments.