一种比例再保险和投资最优化问题

假设保险盈余服从跳跃扩散过程,保险资金投资标的包括无风险资产和风险资产两部分,其中股票价格过程服从CEV模型.本文研究了一种终值财富期望指数效用最大化的最优化比例再保险投资问题.利用随机控制理论技术,得到比例再保险投资过程的HJB方程,并从理论上推导出了最优投资策略和价值函数的显示表达式.     

CEV模型下时滞最优投资与再保险问题

在常方差弹性（constant elasticity of variance,CEV）模型下考虑了时滞最优投资与比例再保险问题.假设保险公司通过购买比例再保险对保险索赔风险进行管理,并将其财富投资于一个无风险资产和一个风险资产组成的金融市场,其中风险资产的价格过程服从常方差弹性模型.考虑与历史业绩相关的现金流量,保险公司的财富过程由一个时滞随机微分方程刻画,在负指数效用最大化的目标下求解了时滞最优投资与再保险控制问题,分别在投资与再保险和纯投资两种情形下得到最优策略和值函数的解析表达式.最后通过数值算例进一步说明主要参数对最优策略和值函数的影响.     

相依风险模型下具有延迟和违约风险的鲁棒最优投资和再保险策略（英文）

本文研究了在风险相依模型下具有延迟和违约风险的鲁棒最优投资再保险策略.假设模糊厌恶型保险人的财富过程有两类相依的保险业务并且余额可以投资于无风险资产、可违约债券和价格过程遵循Heston模型的风险资产.利用动态规划原则,我们分别建立了违约后和违约前的鲁棒HJB方程.另外,通过最大化终端财富的期望指数效用,我们得到了最优投资和再保险策略以及相应的值函数.最后,通过一些数值例子说明了某些模型参数对鲁棒最优策略的影响.     

具有随机利率、随机变差的最优投资和联合比例-超额损失再保险

对跳-扩散风险模型,研究了最优投资和再保险问题.保险公司可以购买再保险减少理赔,保险公司还可以把盈余投资在一个无风险资产和一个风险资产上.假设再保险的方式为联合比例-超额损失再保险.还假设无风险资产和风险资产的利率是随机的,风险资产的方差也是随机的.通过解决相应的Hamilton-Jacobi-Bellman(HJB)方程,获得了最优值函数和最优投资、再保险策略的显示解.特别的,通过一个例子具体的解释了得到的结论.     

CEV模型下时滞最优投资与再保险问题

在常方差弹性(constant elasticity of variance,CEV)模型下考虑了时滞最优投资与比例再保险问题.假设保险公司通过购买比例再保险对保险索赔风险进行管理,并将其财富投资于一个无风险资产和一个风险资产组成的金融市场,其中风险资产的价格过程服从常方差弹性模型.考虑与历史业绩相关的现金流量,保险公司的财富过程由一个时滞随机微分方程刻画,在负指数效用最大化的目标下求解了时滞最优投资与再保险控制问题,分别在投资与再保险和纯投资两种情形下得到最优策略和值函数的解析表达式.最后通过数值算例进一步说明主要参数对最优策略和值函数的影响.     

带交易费用的最优投资和比例再保险

研究了保险公司的最优投资和再保险问题.保险公司的盈余通过跳-扩散风险模型来模拟,可以把盈余的一部分投资到金融市场,金融市场由一个无风险资产和n个风险资产组成,并且保险公司还可以购买比例再保险;在买卖风险资产时,考虑了交易费用.通过随机控制的理论,获得了最优策略和值函数的显示解.     

通胀风险下的鲁棒最优投资组合与再保险问题研究（英文）

本文研究了一个保险公司带通胀风险的鲁棒最优投资组合与再保险问题,其中保险公司对模型不确定性是含糊厌恶的.我们假设保险公司不仅可以购买比例再保险,还可以在风险资产和无风险资产中进行投资.在模型不确定性框架中,本文的优化目标是使得保险公司的终端财富最小的情况下其幂效用达到最大.根据随机控制理论,获得了最优策略和值函数的显示表达式.     

基于损失相依保费原则下的最优再保险-投资策略

本文研究了基于损失相依保费原则下的最优再保险投资问题。该保费原则是基于过去的损失和对未来损失的估计来动态地更新保费，是传统的期望值保费原则的一个拓展。我们假设保险公司的盈余过程遵循C-L(Cramér-Lundberg)模型的扩散近似，保险公司通过购买比例再保险或获得新业务来分散风险或增加收益。假设金融市场由一个无风险资产和一个风险资产组成，其中风险资产的价格过程由仿射平方根随机模型描述。我们以最大化保险公司的终端时刻财富的期望效用为目标，利用动态规划，随机控制等方法得到CARA效用函数下的值函数的解析解，并得到最优再保险和投资策略的显性表达式。最后通过数值算例，分析了部分模型参数对最优再保险投资策略的影响。     

Vasicek利率与Heston模型下的最优投资和再保险

本文主要研究Vasicek随机利率模型下保险公司的最优投资与再保险问题.假设保险公司的盈余过程由带漂移的布朗运动来描述,保险公司通过购买比例再保险来转移索赔风险;同时,将财富投资于由一种无风险资产与一种风险资产组成的金融市场,其中,利率期限结构服从Vasicek利率模型,且风险资产价格过程满足Heston随机波动率模型.利用动态规划原理及变量替换的方法,得到了指数效用下最优投资与再保险策略的显示表达式,并给出数值例子分析了主要模型参数对最优策略的影响.     

扩散风险模型下再保险和投资对红利的影响

对扩散风险模型,研究了比例再保险和投资对红利的影响．在常数边界分红策略下,得到了使得期望贴现红利最大的最优比例再保险和投资策略的显示表达式,并得到最大期望贴现红利的显示表达式．最后,通过数值计算得到了再保险和投资对期望红利的影响,以及最优投资策略与各参数之间的关系．     

Optimal Pricing for Optimal Transport

Suppose that c(x, y) is the cost of transporting a unit of mass from x ∈ X to y ∈ Y and suppose that a mass distribution μ on X is transported optimally (so that the total cost of transportation is minimal) to the mass distribution ν on Y. Then, roughly speaking, the Kantorovich duality theorem asserts that there is a price f(x) for a unit of mass sold (say by the producer to the distributor) at x and a price g(y) for a unit of mass sold (say by the distributor to the end consumer) at y such that for any x ∈ X and y ∈ Y, the price difference g(y) ? f(x) is not greater than the cost of transportation c(x, y) and such that there is equality g(y) ? f(x) = c(x, y) if indeed a nonzero mass was transported (via the optimal transportation plan) from x to y. We consider the following optimal pricing problem: suppose that a new pricing policy is to be determined while keeping a part of the optimal transportation plan fixed and, in addition, some prices at the sources of this part are also kept fixed. From the producers’ side, what would then be the highest compatible pricing policy possible? From the consumers’ side, what would then be the lowest compatible pricing policy possible? We have recently introduced and studied settings in c-convexity theory which gave rise to families of c-convex c-antiderivatives, and, in particular, we established the existence of optimal c-convex c-antiderivatives and explicit constructions of these optimizers were presented. In applications, it has turned out that this is a unifying language for phenomena in analysis which used to be considered quite apart. In the present paper we employ optimal c-convex c-antiderivatives and conclude that these are natural solutions to the optimal pricing problems mentioned above. This type of problems drew attention in the past and existence results were previously established in the case where X = Y = ? ⁿ under various specifications. We solve the above problem for general spaces X, Y and real-valued, lower semicontinuous cost functions c. Furthermore, an explicit construction of solutions to the general problem is presented.     

Optimal sharing

We investigate a sharing method to distribute a given quantity of resources equitably through a capacity-constrained distribution network. The sharing, called an optimal sharing, not only maximizes the minimum share but also minimizes the maximum share. The optimal sharing is obtained in time O(|T| c(n e)) where |T| is the number of sinks in the network andc(n, e) is the time required to solve the maximum flow problem.     

Optimal endpoints

A complete set of necessary and sufficient conditions for selecting optimal endpoints for extremals obtained from the variational Bolza problem in control notation has been developed. The method used to obtain these conditions is based on a seldom used concept of performing a dichotomy on the general optimization problem. With this concept, the problem of Bolza is decomposed into two problems, the first of which involves the selection of optimal paths with the endpoints considered fixed. The second problem involves the selection of optimal endpoints with the paths between the endpoints taken to be stationary curves. The convenience of the dichotomy in deriving the necessary and sufficient conditions for endpoints lies in its simplicity and elementary character; well-known necessary and sufficient conditions from the theory of ordinary maxima and minima are used.An endpoint necessary condition is first obtained which is simply the well-known transversality condition. An additional condition is then developed which, together with the transversality condition, leads to a set of necessary and sufficient conditions for a given extremal to be locally optimal with respect to endpoint variations. While the second condition presented is akin to the classical focal-point condition, the result is new in form and is directly applicable to the optimal control problem. In addition, it is relatively simple to apply and is easy to implement numerically when an analytical solution is not possible. It should be useful in situations where the transversality conditions yield more than one choice for an optimal endpoint.An analytic solution for a simple geodetics problem is presented to illustrate the theory. A discussion of numerical implementation of the sufficiency conditions and its application to an orbit transfer example is also included.This work was supported in part by the National Aeronautics and Space Administration, Grant No. NGR-03-002-001.     

Optimal partitions

Consider a set of numbersZ={z ₁≥z ₂≥...≥z _n} and a functionf defined on subsets ofZ. LetP be a partition ofZ into disjoint subsetsS _i, say,g of them. The cost ofP is defined as $$C(P) = \sum\limits_{i = 1}^g {f(S_i )} .$$ By definition, in anordered partition, every pair of subsets has the property that the numbers in one subset are all greater than or equal to every number in the other subset. The problem of minimizingC(P) over all ordered partitions is called the optimal ordered partition problem. While no efficient method is known for solving the general optimal partition problem, the optimal ordered partition problem can be solved in quadratic time by dynamic programming. In this paper, we study the conditions onf under which an optimal ordered partition is indeed an optimal partition. In particular, we present an additive model and a multiplicative model for the functionf and give conditions such that the optimal partition problem can be reduced to the optimal ordered partition problem. We illustrate our results by applying them on problems which have been investigated previously in the literature.     

随机递归最优控制和混合最优控制问题

对随机递归最优控制问题即代价函数由特定倒向随机微分方程解来描述和递归混合最优控制问题即控制者还需 决定最优停止时刻, 得到了最优控制的存在性结果. 在一类等价概率测度集中,还给出了递归最优值函数的最小和最大数学期望.     

Optimal Value and Post Optimal Solution in a Transportation Problem

In this work, we analyse the transportation problem of a real-life situation by obtaining the optimal feasible solutions, thus carrying out the sensitivity analysis of the problem. The work utilises the data obtained from the Asejire and Ikeja plants of Coca-Cola company, aiming to aid decision-making regarding the best possible options to satisfy customers at the barest minimum cost of transportation. Rerunning the optimization of a problem is an expensive scheme for gathering and obtaining enough data required for a problem. Thus, to minimize the transportation cost, the sensitivity analysis of parameters is a good tool to determine the behaviour of some input parameters where the values of these parameters are varied arbitrarily such that optimal results are verified. Maple 18 Software is used to solve the problem and the result obtained is compared with the values evaluated from northwest corner method, least cost method and Vogel''s approximation method. The study critically shows how a little change in a unit or more of any model parameter affects the expected results.     

Optimal Delaunay Triangulations

The Delaunay triangulation, in both classic and more generalized sense, is studied in this paper for minimizing the linear interpolation error (measure in L^P-norm) for a given function. The classic Delaunay triangulation can then be characterized as an optimal triangulation that minimizes the interpolation error for the isotropic function ‖x‖^2 among all the triangulations with a given set of vertices. For a more general function, a functiondependent Delaunay triangulation is then defined to be an optimal triangulation that minimizes the interpolation error for this function and its construction can be obtained by a simple lifting and projection procedure. The optimal Delaunay triangulation is the one that minimizes the interpolation error among all triangulations with the same number of vertices, i.e. the distribution of vertices are optimized in order to minimize the interpolation error. Such a function-depend entoptimal Delaunay triangulation is proved to exist for any given convex continuous function.On an optimal Delaunay triangulation associated with f, it is proved that △↓f at the interior vertices can be exactly recovered by the function values on its neighboring vertices.Since the optimal Delaunay triangulation is difficult to obtain in practice, the concept of nearly optimal triangulation is introduced and two sufficient conditions are presented for a triangulation to be nearly optimal.     

Optimal popular matchings

In this paper we consider the problem of computing an “optimal” popular matching. We assume that our input instance admits a popular matching and here we are asked to return not any popular matching but an optimal popular matching, where the definition of optimality is given as a part of the problem statement; for instance, optimality could be fairness in which case we are required to return a fair popular matching. We show an O(n²+m) algorithm for this problem, assuming that the preference lists are strict, where m is the number of edges in G and n is the number of applicants.     

Optimal Financial Portfolios

The classes of reward‐risk optimization problems that arise from different choices of reward and risk measures are considered. In certain examples the generic problem reduces to linear or quadratic programming problems. An algorithm based on a sequence of convex feasibility problems is given for the general quasi‐concave ratio problem. Reward‐risk ratios that are appropriate in particular for non‐normal assets return distributions and are not quasi‐concave are also considered.     

Optimal key systems

A key system is represented by an ordered rooted tree. We construct trees minimizing relevant cost functions. Our application concerns interactive voice response (IVR), or automated telephone operators, for navigation purposes.