Risk minimization for an insurer with investment and reinsurance via g-expectation

Abstract

This paper is devoted to the study of a risk-based optimal investment and proportional reinsurance problem. The surplus process of the insurer and the risky asset process in the financial market are assumed to be general jump-diffusion processes. We use a convex risk measure generated by g-expectation to describe the risk of the terminal wealth with investment and reinsurance. Under the aim of minimizing the risk, the problem is solved by using techniques of stochastic maximum principles. Two interesting special cases are studied and the explicit expressions for optimal strategies and corresponding minimal risks are derived.     

Optimal investment-consumption and life insurance with capital constraints

Abstract

The aim of this paper is to solve an optimal investment, consumption and life insurance problem when the investor is restricted to capital guarantee. We consider an incomplete market described by a jump-diffusion model with stochastic volatility. Using the martingale approach, we prove the existence of the optimal strategy and the optimal martingale measure and we obtain the explicit solutions for the power utility functions.     

On Sampling Designs for Integral Estimation of a Random Process

Abstract

In this paper the problem of finding exactly optimal sampling designs for estimating the weighted integral of a stochastic process with a product covariance structure (R(s,t)=u(s)v(t), s<t) is discussed. The sampling designs for certain standard processes belonging to the product class are calculated. An asymptotic solution to the design problem also follows as a consequence.     

Optimization of continuous and discrete scheduled times for a cumulative damage system with age-dependent maintenance

Abstract

This paper presents a preventive replacement problem when a system is operating successive works with random times and suffering stochastic shocks. The works cause random amount additive damage to the system, and the system fails whenever the cumulative damage reaches a failure level threshold. As an external shock occurs, the system experiences one of the two types of shocks with age-dependent maintenance mechanism: type-I (minor) shock is rectified by a minimal repair, or type-II (catastrophic) shock causes the system to fail. To control the deterioration process, preventive replacement is scheduled to replace the system at a continuous age T or at a discrete number N of working cycles, whichever occurs first, and corrective replacement is performed immediately whenever the system fails due to either shock or damage. The optimal preventive replacement schedule that minimizes the expected cost rate is discussed analytically and computed numerically. The proposed model provides a general framework for analyzing maintenance policies and extends several existing results.     

Functionals of Markovian Branching D-BMAPS

Abstract

We consider a stochastic system in which Markovian customer attribute processes are initiated at customer arrivals in a discrete batch Markovian arrival process (D-BMAP). We call the aggregate a Markovian branching D-BMAP. Each customer attribute process is an absorbing discrete time Markov chain whose parameters depend both on the phase transition, of the driving D-BMAP, and the number of arrivals taking place at the customer's arrival instant. We investigate functionals of Markovian branching D-BMAPs that may be interpreted as cumulative rewards collected over time for the various customers that arrive to the system, in the transient and asymptotic cases. This is achieved through the derivation of recurrence relations for expected values and Laplace transforms in the former case, and Little's law in the latter case.     

An evolutionary algorithm for A-optimal incomplete block designs

Evolutionary algorithms are heuristic stochastic search and optimization techniques with principles taken from natural genetics. They are procedures mimicking the evolution process of an initial population through genetic transformations. This paper is concerned with the problem of finding A-optimal incomplete block designs for multiple treatment comparisons represented by a matrix of contrasts. An evolutionary algorithm for searching optimal, or nearly optimal, incomplete block designs is described in detail. Various examples regarding the application of the algorithm to some well-known problems illustrate the good performance of the algorithm     

Mean-variance problem for an insurer with default risk under a jump-diffusion risk model

Abstract

This paper considers an optimal investment-reinsurance problem with default risk under the mean-variance criterion. We assume that the insurer is allowed to purchase proportional reinsurance and invest his/her surplus in a risk-free asset, a stock and a defaultable bond. The goal is to maximize the expectation and minimize the variance of the terminal wealth. We first formulate the problem to stochastic linear-quadratic (LQ) control problem with constraints. Then the optimal investment-reinsurance strategies and the corresponding value functions are obtained via the viscosity solutions of Hamilton-Jacobi-Bellman (HJB) equations for the post-default case and pre-default case, respectively. Finally, we provide numerical examples to illustrate the effects of model parameters on the optimal strategies and value functions.     

Print Magazines for American College Libraries

Abstract

This paper opens discussion about the periodicals that are left behind in the debate over the transition from print to electronic journals in academic libraries, particularly college libraries. The author annotates 100 English-language print magazines titles that support a liberal arts curriculum and the leisure reading of an American college community. These titles should be maintained in print versions for browsing and usefulness, even if online availability exists. Magazines, with their mix of articles, illustrations, sidebars, tables, charts, graphs, lists, and short features, still have an important place in college libraries.     

A sampling plan for one-shot systems considering destructive inspection

Abstract

The paper is concerned with an acceptance sampling problem under destructive inspections for one-shot systems. The systems may fail at random times while they are operating (as the systems are considered to be operating when storage begins), and these failures can only be identified by inspection. Thus, n samples are randomly selected from N one-shot systems for periodic destructive inspection. After storage time T, the N systems are replaced if the number of working systems is less than a pre-specified threshold k. The primary purpose of this study is to determine the optimal number of samples n*, extracted from the N for destructive detection and the optimal acceptance number k*, in the sample under the constraint of the system interval availability, to minimize the expected cost rate. Numerical experiments are studied to investigate the effect of the parameters in sampling inspection on the optimal solutions.     

On Uniformly Optimal Networks: A Reversal of Fortune?

In this article, the general problem of comparing the performance of two communication networks is examined. The standard approach, using stochastic ordering as a metric, is reviewed, as are the mixed results on the existence of uniformly optimal networks (UONs) which have emerged from this approach. While UONs have been shown to exist for certain classes of networks, it has also been shown that no UON network exists for other classes. Results to date beg the question: Is the problem of identifying a Uniformly Optimal Network (UON) of a given size dead or alive? We reframe the investigation into UONs in terms of network signatures and the alternative metric of stochastic precedence. While the endeavor has been dead, or at least dormant, for some 20 years, the findings in the present article suggest that the question above is by no means settled. Specifically, we examine a class of networks of a particular size for which it was shown that no individual network was uniformly optimal relative to the standard metric (the uniform ordering of reliability polynomials), and we show, using the aforementioned alternative metric, that this class is totally ordered and that a uniformly optimal network exists after all. Optimality with respect to “performance per unit cost” type metrics is also discussed.     

Estimation of parameters of SDE driven by fractional Brownian motion with polynomial drift

ABSTRACT

Strongly consistent and asymptotically normal estimators of the Hurst index and volatility parameters of solutions of stochastic differential equations with polynomial drift are proposed. The estimators are based on discrete observations of the underlying processes.     

Bootstrapping stochastic regression models under homoskedasticity: wild bootstrap vs. pairs bootstrap

We investigate by simulation how the wild bootstrap and pairs bootstrap perform in t and F tests of regression parameters in the stochastic regression model, where explanatory variables are stochastic and not given and there exists no heteroskedasticity. The wild bootstrap procedure due to Davidson and Flachaire [The wild bootstrap, tamed at last, Working paper, IER#1000, Queen's University, 2001] with restricted residuals works best but its dominance is not strong compared to the result of Flachaire [Bootstrapping heteroskedastic regression models: wild bootstrap vs. pairs bootstrap, Comput. Statist. Data Anal. 49 (2005), pp. 361–376] in the fixed regression model where explanatory variables are fixed and there exists heteroskedasticity.     

On stochastic behaviors of load-sharing parallel systems

Abstract

This paper mainly investigates a general load-sharing parallel system having two units. First, we construct some comparisons among a load standby system, a warm standby system, a hot standby system and a cold standby system. Moreover, some stochastic comparisons between the load-sharing parallel system and one of its two components are obtained in the sense of the usual stochastic order. Finally, the residual life of this system and its properties are examined.     

Presto: a software package for the simulation of diffusion processes

Conclusion Presto is a software which automatically generates FORTRAN code corresponding to approximation procedures of the solutions of stochastic differential systems.At the present time, it answers only to a few needs, but a diversification of its users and its simple internal structure could easily permit it to be developed towards a more ambitious system.Finally, let us mention that Presto is an INRIA product, which is free for academic institutions, universities, etc, which already have MAPLE and X-Windows licences. Presto can be run on any UNIX station under X-Windows environment.     

2011 Kansas Library Association Annual Meeting

Abstract

The annual meeting of the Kansas Library Association (KLA) was held April 6–8, 2011, in Topeka, KS, giving a brief respite and spring rejuvenation to academic and public librarians in the state.     

Ordering k-out-of-n systems with interdependent components and one active redundancy

This paper studies the optimal allocation of one active redundancy to a k-out-of-n system in the context of statistically dependent component lifetimes. It is proved that assigning the redundancy to the weakest component is more favorable so as to get a larger system lifetime in terms of both the usual stochastic order and the stochastic preference order.     

Equilibrium probabilities for a production-inventory system maintained by a control-limit policy

Abstract

In this paper we consider a manufacturing system in which an input generator supplies at a constant rate a buffer with a raw material and a production unit pulls the raw material from the buffer at a stochastic rate. We consider specific control-limit policies for the maintenance of the production unit. We show that the equilibrium probabilities of the system can be computed exactly when the production unit after a maintenance remains idle until the buffer is filled up.     

Hedging of contingent claims written on non traded assets under Markov-modulated models

ABSTRACT

This paper studies the hedging problem of European contingent claims when the underlying asset is non traded. We assume that the share prices of the assets are governed by Markov-modulated processes; that is, the market parameters switch over the time according to a finite-state continuous time Markov chain. Due to the presence of Markov chain the non traded asset, the market which we consider is incomplete, we shall use the local risk minimization method to obtain an optimal hedging strategy in a closed-form for an investor. Finally, numerical illustrations of an optimal hedging strategy are given by the Monte Carlo simulation.     

Statistical estimation with bounded memory

We investigate bounded-memory estimators of statistical functionals. It is shown that, for nondegenerate functionals and stochastic processes, it is impossible to achieve consistent estimation with bounded memory. In the positive direction, we show that O(log(1/??)) states suffice to achieve ??-consistent estimation for a natural class of functionals. A?canonical optimal construction is conjectured for arbitrary statistical functionals.     

Quadratic reflected BSDEs and related obstacle problems for PDEs

Abstract

In this paper, we study a kind of reflected backward stochastic differential equations (BSDEs) whose generators are of quadratic growth in z and linear growth in y. We first give an estimate of solutions to such reflected BSDEs. Then under the condition that the generators are convex with respect to z, we can obtain a comparison theorem, which implies the uniqueness of solutions for this kind of reflected BSDEs. Besides, the assumption of convexity also leads to a stability property in the spirit of above estimate. We further establish the nonlinear Feynman-Kac formula of the related obstacle problems for partial differential equations (PDEs) in our framework. At last, a numerical example is given to illustrate the applications of our theoretical results, as well as its connection with an optimal stopping time problem.