Optimal Investment Strategies for an Insurer with SAHARA Utility

In this paper, we consider the optimal investment strategy which maximizes the utility of the terminal wealth of an insurer with SAHARA utility functions. This class of utility functions has non-monotone absolute risk aversion, which is more flexible than the CARA and CRRA utility functions. In the case that the risk process is modeled as a Brownian motion and the stock process is modeled as a geometric Brownian motion, we get the closed-form solutions for our problem by the martingale method for both the constant threshold and when the threshold evolves dynamically according to a specific process. Finally, we show that the optimal strategy is state-dependent.     

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??In this paper, we consider the optimal investment strategy which maximizes the utility of the terminal wealth of an insurer with SAHARA utility functions. This class of utility functions has non-monotone absolute risk aversion, which is more flexible than the CARA and CRRA utility functions. In the case that the risk process is modeled as a Brownian motion and the stock process is modeled as a geometric Brownian motion, we get the closed-form solutions for our problem by the martingale method for both the constant threshold and when the threshold evolves dynamically according to a specific process. Finally, we show that the optimal strategy is state-dependent.     

Optimal proportional reinsurance and investment under partial information

In this paper, we study the optimal proportional reinsurance and investment strategy for an insurer that only has partial information at its disposal, under the criterion of maximizing the expected utility of the terminal wealth. We assume that the surplus of the insurer is governed by a jump diffusion process, and that reinsurance is used by the insurer to reduce risk. In addition, the insurer can invest in financial markets. We give a characterization for the optimal strategy within a non-Markovian setting. Malliavin calculus for Lévy processes is used for the analysis.     

Minimizing the probability of lifetime ruin under borrowing constraints

We determine the optimal investment strategy of an individual who targets a given rate of consumption and who seeks to minimize the probability of going bankrupt before she dies, also known as lifetime ruin. We impose two types of borrowing constraints: First, we do not allow the individual to borrow money to invest in the risky asset nor to sell the risky asset short. However, the latter is not a real restriction because in the unconstrained case, the individual does not sell the risky asset short. Second, we allow the individual to borrow money but only at a rate that is higher than the rate earned on the riskless asset.We consider two forms of the consumption function: (1) The individual consumes at a constant (real) dollar rate, and (2) the individual consumes a constant proportion of her wealth. The first is arguably more realistic, but the second is closely connected with Merton’s model of optimal consumption and investment under power utility. We demonstrate that connection in this paper, as well as include a numerical example to illustrate our results.     

考虑企业释放质量信号行为的产品推广策略

为吸引消费者, 一些企业尝试以释放质量信号为手段进行产品推广。本文考虑消费者购买时的参考效用, 通过构建模型, 探讨了短期经营下低质量企业不释放质量信号、短期经营下低质量企业释放质量信号、长期经营下低质量企业不释放质量信号和长期经营下低质量企业释放质量信号等四种情况下的产品定价策略, 并分析了释放质量信号对企业运营带来的利弊。研究发现:长期经营下低质量企业释放质量信号时, 产品质量差距的扩大将提高竞争企业的最优定价, 而释放质量信号程度的增加则将使最优定价降低。同时, 通过释放质量信号, 短期内低质量企业看似可以借此获得大量需求, 但现实中可行性不高。从长期经营来看, 以释放质量信号为手段的推广策略实际上会损害整个市场的利益。     

Representing Utility Functions via Weighted Goals

We analyze the expressivity, succinctness, and complexity of a family of languages based on weighted propositional formulas for the representation of utility functions. The central idea underlying this form of preference modeling is to associate numerical weights with goals specified in terms of propositional formulas, and to compute the utility value of an alternative as the sum of the weights of the goals it satisfies. We define a large number of representation languages based on this idea, each characterized by a set of restrictions on the syntax of formulas and the range of weights. Our aims are threefold. First, for each language we try to identify the class of utility functions it can express. Second, when different languages can express the same class of utility functions, one may allow for a more succinct representation than another. Therefore, we analyze the relative succinctness of languages. Third, for each language we study the computational complexity of the problem of finding the most preferred alternative given a utility function expressed in that language (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Moments of utility functions and their applications

This paper presents moments and cross-moments of utility functions and measures of utility dependence. We start with an interpretation of the nth moment of a utility function, and describe methods for its assessment in practice and consistency checks that need to be satisfied for any assessed moments. We then show how moments of a utility function (i) provide a new method to determine the parameters of a given functional form of a utility function and (ii) to derive the functional form of a utility function that satisfies some given moment assessments. Next, we derive a fundamental formula that relates the expected utility of a joint distribution to the expected utility of the marginal distributions for multiattribute utility functions. We use this formulation to provide an intuitive interpretation for cross-moments of utility functions and illustrate their use in (i) constructing multiattribute utility functions that incorporate utility dependence and (ii) in providing necessary conditions for utility independence in decisions with multiple attributes. We end with a new measure of utility dependence for multiattribute utility functions and work through several examples to illustrate the approach.     

Inheritance of properties in NTU communication situations

In this paper we consider communication situations in which utility is nontransferable. We compare this model with the more familiar model of transferable utility communication situations in terms of the corresponding graph-restricted games. We extend transferable utility results on the inheritance of properties of the underlying game to the graph-restricted game to our context of nontransferable utility.Thanks are due to Peter Borm for some helpful comments.     

On optimal investment with processes of long or negative memory

We consider the problem of utility maximization for investors with power utility functions. Building on the earlier work Larsen et al. (2016), we prove that the value of the problem is a Fréchet-differentiable function of the drift of the price process, provided that this drift lies in a suitable Banach space.We then study optimal investment problems with non-Markovian driving processes. In such models there is no hope to get a formula for the achievable maximal utility. Applying results of the first part of the paper we provide first order expansions for certain problems involving fractional Brownian motion either in the drift or in the volatility. We also point out how asymptotic results can be derived for models with strong mean reversion.     

Optimal Control for Utility Portfolio Selection with Liability

In this paper we use stochastic optimal control theory to investigate a dynamic portfolio selection problem with liability process, in which the liability process is assumed to be a geometric Brownian motion and completely correlated with stock prices. We apply dynamic programming principle to obtain Hamilton-Jacobi-Bellman (HJB) equations for the value function and systematically study the optimal investment strategies for power utility, exponential utility and logarithm utility. Firstly, the explicit expressions of the optimal portfolios for power utility and exponential utility are obtained by applying variable change technique to solve corresponding HJB equations. Secondly, we apply Legendre transform and dual approach to derive the optimal portfolio for logarithm utility. Finally, numerical examples are given to illustrate the results obtained and analyze the effects of the market parameters on the optimal portfolios.     

Utility maximization problem in the case of unbounded endowment

We consider a problem of expected utility maximization with an utility function finite on ?₊ and with an unbounded random endowment in an abstract model of financial market. We formulate a dual problem to the primal one and prove duality relations between them. In addition, we study necessary conditions to the existence of solutions to the primal problem. Finally, we reduce the dual problem to a form more convenient for practice.     

Optimising a nonlinear utility function in multi-objective integer programming

In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the optimal utility value. This is done using already known solutions, linear programming relaxations, utility function inversion, and integer programming. We develop a general optimisation algorithm for use with k objectives, and we illustrate our approach using a tri-objective integer programming problem.     

Solving linear-quadratic conditional Gaussian influence diagrams

This paper considers the problem of solving Bayesian decision problems with a mixture of continuous and discrete variables. We focus on exact evaluation of linear-quadratic conditional Gaussian influence diagrams (LQCG influence diagrams) with additively decomposing utility functions. Based on new and existing representations of probability and utility potentials, we derive a method for solving LQCG influence diagrams based on variable elimination. We show how the computations performed during evaluation of a LQCG influence diagram can be organized in message passing schemes based on Shenoy–Shafer and Lazy propagation. The proposed architectures are the first architectures for efficient exact solution of LQCG influence diagrams exploiting an additively decomposing utility function.     

Two axiomatic approaches to decision making using possibility theory

This paper proposes a utility theory for decision making under uncertainty that is described by possibility theory. We show that our approach is a natural generalization of the two axiomatic systems that correspond to pessimistic and optimistic decision criteria proposed by Dubois et al. The generalization is achieved by removing axioms that are supposed to reflect attitudes toward uncertainty, namely, pessimism and optimism. In their place we adopt an axiom that imposes an order on a class of canonical lotteries that realize either in the best or in the worst prize. We prove an expected utility theorem for the generalized axiomatic system based on the newly introduced concept of binary utility.     

A stochastic dynamic programming approach to decision making in arranged marriages

We employ a stochastic dynamic programming approach to study decision making by an individual wishing to have an arranged marriage. First, we show that this individual never opts out of a voluntarily agreed upon marriage. Second, we demonstrate that our marrying individual uses a reservation utility to determine which marriage proposal to accept. Third, we compute the expected length of time during which our marrying individual stays single. Finally, we focus on an arranged marriage market in which there are many identical marrying individuals and profit maximizing matchmaking firms. We show that profit maximization implies that all matchmaking firms offer marriage proposals whose utility equals the reservation utility of our marrying individuals.     

Parametric network utility maximization problem

We show how to solve the parametric utility maximization problem with a continuous parameter in a finite number of steps in order to obtain a solution with given accuracy. Also, we propose a new approach for the discretization of time for the parametric utility maximization problem with Lipschitz utility function. Some numerical results are provided.     

Optimal Compensation with Hidden Action and Lump-Sum Payment in a Continuous-Time Model

We consider a problem of finding optimal contracts in continuous time, when the agent’s actions are unobservable by the principal, who pays the agent with a one-time payoff at the end of the contract. We fully solve the case of quadratic cost and separable utility, for general utility functions. The optimal contract is, in general, a nonlinear function of the final outcome only, while in the previously solved cases, for exponential and linear utility functions, the optimal contract is linear in the final output value. In a specific example we compute, the first-best principal’s utility is infinite, while it becomes finite with hidden action, which is increasing in value of the output. In the second part of the paper we formulate a general mathematical theory for the problem. We apply the stochastic maximum principle to give necessary conditions for optimal contracts. Sufficient conditions are hard to establish, but we suggest a way to check sufficiency using non-convex optimization.     

"边信息"的效用优化及其影响

本文考虑受随机因素影响的股票价模型 ,投资者仅知道的股价信息 (公共信息 )和“边信息”的效用优化问题 .我们利用测度的变换和投影 ,给出了具有“边信息”和不具“边信息”两种情况下的最优财富形式 .对于对数效用函数 ,我们比较最优效用 ,讨论了“边信息”的影响     

A numerical approach to utility functions in risk theory

Given the standard equilibrium model for an insurance market and sharing rules defining a feasible risk-exchange, we want to determine numerically the utility functions leading to the equilibrium. In the special case of two companies we approximate the sharing rules by piecewise linear functions and give an algorithm to compute piecewise quadratic utility functions which are solutions of the equilibrium model. We apply our method to compare some insurance contracts. For this we introduce the notion of acceptability of an insurance contract and a risk equivalence property based on utility theory. The numerical examples lead to interesting interpretations which give some insight in the considered insurance contracts.