A switched linear quadratic（LQ） differential game over finite-horizon is investigated in this paper. The switching signal is regarded as a non-conventional player, afterwards the definition of Pareto efficiency is e...A switched linear quadratic（LQ） differential game over finite-horizon is investigated in this paper. The switching signal is regarded as a non-conventional player, afterwards the definition of Pareto efficiency is extended to dynamics switching situations to characterize the solutions of this multi-objective problem. Furthermore, the switched differential game is equivalently transformed into a family of parameterized single-objective optimal problems by introducing preference information and auxiliary variables. This transformation reduces the computing complexity such that the Pareto frontier of the switched LQ differential game can be constructed by dynamic programming. Finally, a numerical example is provided to illustrate the effectiveness.展开更多
This paper examines moral hazard problems in team setting. It is shown that there may exist budget balancing Nash equilibrium sharing rules that yield Pareto optimal (first best) efficiency provided that any of the f...This paper examines moral hazard problems in team setting. It is shown that there may exist budget balancing Nash equilibrium sharing rules that yield Pareto optimal (first best) efficiency provided that any of the following three conditions is satisfied: if peer pressure plays the role of mutual monitoring, or if agents over estimate the effects of their actions on jointed production, or if agents are sufficiently risk averse. The role played by the monitors in inducing first best efficiency is also discussed.展开更多
This papcr investigates a Parcto optimal insurancc contract design problcm within a behavioral finance framework.In this context,the insured evaluates contracts using the rank-dependent utility(RDU,for short)theory,wh...This papcr investigates a Parcto optimal insurancc contract design problcm within a behavioral finance framework.In this context,the insured evaluates contracts using the rank-dependent utility(RDU,for short)theory,while the insurer applies the expected value premium principle.The analysis incorporates the incentive compatibility constraint,ensuring that the contracts,called moral-hazard-free,are free from the moral hazard issues identified in Bernard et al.[4].Initially,the problem is formulated as a nonconcave maximization problem involving Choquet expectation.It is then transformed into a quantile optimization problem and addrcssed using thc calculus of variations mcthod.The optimal contracts are characterized by a double-obstacle ordinary differential equation for a semi-linear second-order elliptic operator with nonlocal boundary conditions,which seems new in the financial economics literature.We present a straightforward numerical scheme and a numerical example to compute the optimal contracts.Let and mo represent the relative safety loading and the mass of the potential loss at O,respectively.We discover that every moral-hazard-free contract is optimal for infinitely many RDU-insured individuals if 0<θ<m_(0)/1-m_(0).Conversely,certain contracts,such as the full coverage contract,are never optimal for any RDU-insured individual ifθ>m_(0)/1-m_(0)Additionally,we derive all the Pareto optimal contracts when either the compensation or the retention violates the monotonicity constraint.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.61773098the 111 Project under Grant No.B16009
文摘A switched linear quadratic（LQ） differential game over finite-horizon is investigated in this paper. The switching signal is regarded as a non-conventional player, afterwards the definition of Pareto efficiency is extended to dynamics switching situations to characterize the solutions of this multi-objective problem. Furthermore, the switched differential game is equivalently transformed into a family of parameterized single-objective optimal problems by introducing preference information and auxiliary variables. This transformation reduces the computing complexity such that the Pareto frontier of the switched LQ differential game can be constructed by dynamic programming. Finally, a numerical example is provided to illustrate the effectiveness.
基金This research is supported by the post doctoral research foundation at the Amos Tuck School ofDartmouth College
文摘This paper examines moral hazard problems in team setting. It is shown that there may exist budget balancing Nash equilibrium sharing rules that yield Pareto optimal (first best) efficiency provided that any of the following three conditions is satisfied: if peer pressure plays the role of mutual monitoring, or if agents over estimate the effects of their actions on jointed production, or if agents are sufficiently risk averse. The role played by the monitors in inducing first best efficiency is also discussed.
基金support from the NSFC(Grant No.11471276,11971409)The Hong Kong RGC(GRF Grant No.15202817,15202421,15204622 and 15203423)+1 种基金the PolyU-SDU Joint Research Center on Financial Mathematics,the CAS AMSS-PolyU Joint Laboratory of Applied Mathematics,the Research Centre for Quantitative Finance(1-CE03)internal grants from The Hong Kong Polytechnic University.
文摘This papcr investigates a Parcto optimal insurancc contract design problcm within a behavioral finance framework.In this context,the insured evaluates contracts using the rank-dependent utility(RDU,for short)theory,while the insurer applies the expected value premium principle.The analysis incorporates the incentive compatibility constraint,ensuring that the contracts,called moral-hazard-free,are free from the moral hazard issues identified in Bernard et al.[4].Initially,the problem is formulated as a nonconcave maximization problem involving Choquet expectation.It is then transformed into a quantile optimization problem and addrcssed using thc calculus of variations mcthod.The optimal contracts are characterized by a double-obstacle ordinary differential equation for a semi-linear second-order elliptic operator with nonlocal boundary conditions,which seems new in the financial economics literature.We present a straightforward numerical scheme and a numerical example to compute the optimal contracts.Let and mo represent the relative safety loading and the mass of the potential loss at O,respectively.We discover that every moral-hazard-free contract is optimal for infinitely many RDU-insured individuals if 0<θ<m_(0)/1-m_(0).Conversely,certain contracts,such as the full coverage contract,are never optimal for any RDU-insured individual ifθ>m_(0)/1-m_(0)Additionally,we derive all the Pareto optimal contracts when either the compensation or the retention violates the monotonicity constraint.
