共查询到10条相似文献,搜索用时 312 毫秒
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《Stochastic Processes and their Applications》2020,130(4):1972-1993
This paper studies explicitly solvable multidimensional optimal stopping problems of sum- and product-type in discrete and continuous time using the monotone case approach. It gives a review on monotone case stopping using the Doob decomposition, resp. Doob–Meyer decomposition in continuous time, also in its multiplicative versions. The approach via these decompositions leads to explicit solutions for a variety of examples, including multidimensional versions of the house-selling and burglar’s problem, the Poisson disorder problem, and an optimal investment problem. 相似文献
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In this paper we consider a general optimal consumption-portfolio selection problem of an infinitely-lived agent whose consumption rate process is subject to subsistence constraints before retirement. That is, her consumption rate should be greater than or equal to some positive constant before retirement. We integrate three optimal decisions which are the optimal consumption, the optimal investment choice and the optimal stopping problem in which the agent chooses her retirement time in one model. We obtain the explicit forms of optimal policies using a martingale method and a variational inequality arising from the dual function of the optimal stopping problem. We treat the optimal retirement time as the first hitting time when her wealth exceeds a certain wealth level which will be determined by a free boundary value problem and duality approaches. We also derive closed forms of the optimal wealth processes before and after retirement. Some numerical examples are presented for the case of constant relative risk aversion (CRRA) utility class. 相似文献
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On reinsurance and investment for large insurance portfolios 总被引:1,自引:0,他引:1
We consider a problem of optimal reinsurance and investment for an insurance company whose surplus is governed by a linear diffusion. The company’s risk (and simultaneously its potential profit) is reduced through reinsurance, while in addition the company invests its surplus in a financial market. Our main goal is to find an optimal reinsurance-investment policy which minimizes the probability of ruin. More specifically, in this paper we consider the case of proportional reinsurance, and investment in a Black-Scholes market with one risk-free asset (bond, or bank account) and one risky asset (stock). We apply stochastic control theory to solve this problem. It transpires that the qualitative nature of the solution depends significantly on the interplay between the exogenous parameters and the constraints that we impose on the investment, such as the presence or absence of shortselling and/or borrowing. In each case we solve the corresponding Hamilton-Jacobi-Bellman equation and find a closed-form expression for the minimal ruin probability as well as the optimal reinsurance-investment policy. 相似文献
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The margin shop arises as a model of margining investment portfolios in a batch, a mandatory end-of-day risk management operation for any prime brokerage firm. The margin-shop scheduling problem is the extension of the preemptive flow-shop scheduling problem where precedence constraints can be introduced between preempted parts of jobs. This paper is devoted to the bipartite case which is equivalent to the problem of finding a maximum red matching that is free of blue–red alternating cycles in a complete bipartite graph with blue and red edges. It is also equivalent to the version of the jump-number problem for bipartite posets where jumps inside only one part should be counted. We show that the unit-time bipartite margin-shop scheduling problem is NP-hard but can be solved in polynomial time if the precedence graph is of degree at most two or a forest. 相似文献
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R. Goldbach 《Applied Mathematics and Optimization》1999,39(1):121-142
We adapt some randomized algorithms of Clarkson [3] for linear programming to the framework of so-called LP-type problems,
which was introduced by Sharir and Welzl [10]. This framework is quite general and allows a unified and elegant presentation
and analysis. We also show that LP-type problems include minimization of a convex quadratic function subject to convex quadratic
constraints as a special case, for which the algorithms can be implemented efficiently, if only linear constraints are present.
We show that the expected running times depend only linearly on the number of constraints, and illustrate this by some numerical
results. Even though the framework of LP-type problems may appear rather abstract at first, application of the methods considered
in this paper to a given problem of that type is easy and efficient. Moreover, our proofs are in fact rather simple, since
many technical details of more explicit problem representations are handled in a uniform manner by our approach. In particular,
we do not assume boundedness of the feasible set as required in related methods.
Accepted 7 May 1997 相似文献
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In this paper we consider a mathematical program with semidefinite cone complementarity constraints (SDCMPCC). Such a problem is a matrix analogue of the mathematical program with (vector) complementarity constraints (MPCC) and includes MPCC as a special case. We first derive explicit formulas for the proximal and limiting normal cone of the graph of the normal cone to the positive semidefinite cone. Using these formulas and classical nonsmooth first order necessary optimality conditions we derive explicit expressions for the strong-, Mordukhovich- and Clarke- (S-, M- and C-)stationary conditions. Moreover we give constraint qualifications under which a local solution of SDCMPCC is a S-, M- and C-stationary point. Moreover we show that applying these results to MPCC produces new and weaker necessary optimality conditions. 相似文献
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Hyeng Keun Koo 《Mathematical Methods of Operations Research》1999,50(2):219-243
This paper studies the consumption and portfolio selection problem of an agent who is liquidity constrained and has uninsurable
income risk in a discrete time setting. It gives properties of optimal policies and presents numerical solutions. The paper,
in particular, shows that liquidity constraints and uninsurable income risk reduce consumption and investment in the risky
asset substantially from the levels for the case where no market imperfections exist. This paper also shows how the agent
evaluates his or her human capital and relates the evaluation to optimal decisions. 相似文献
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Yvonne Choquet-Bruhat Piotr T. Chru?ciel Jos�� M. Mart��n-Garc��a 《Annales Henri Poincare》2011,12(3):419-482
We derive explicit formulae for a set of constraints for the Einstein equations on a null hypersurface, in arbitrary space–time
dimensions n + 1 ≥ 3. We solve these constraints and show that they provide necessary and sufficient conditions so that a spacetime solution
of the Cauchy problem on a characteristic cone for the hyperbolic system of the reduced Einstein equations in wave-map gauge
also satisfies the full Einstein equations. We prove a geometric uniqueness theorem for this Cauchy problem in the vacuum
case. 相似文献