Research Interests:
Research Interests:
The problems inherent in expert systems which model human design processes are discussed. An example of such a system is given with PLEX, a knowledge-based expert system that does initial placement of components on a printed circuit... more
The problems inherent in expert systems which model human design processes are discussed. An example of such a system is given with PLEX, a knowledge-based expert system that does initial placement of components on a printed circuit board. A discussion follows on how dependency-directed backtracking and human-aided machine design are being added to PLEX to help overcome some of the difficulties in modeling a human designer.
Research Interests:
We consider the classical risk model where claims X1, X2, . . . arrive in a compound Poisson process with rateλ. The claims are independent identically distributed non-negative random variables with distribution functionH. We always... more
We consider the classical risk model where claims X1, X2, . . . arrive in a compound Poisson process with rateλ. The claims are independent identically distributed non-negative random variables with distribution functionH. We always assume that the first moment μ1 of the claim-size distribution is finite. Higher momentsμj = ∫ xjH(dx), j = 2, . . ., are assumed finite as necessary in the following. We often writeμ for μ1. We further assume that the claims are independent of the claim-arrivals process. Premium income accrues linearly in time at rate c > 0, and the premium loading factor θ = (c − λμ)/λμ is assumed to be positive. When the surplus at t = 0 is u > 0, the surplus at timet is defined to be
Research Interests:
The purpose of risk sharing is to spread the risk among those involved. The principal, or direct, insurer may pass on some of the risk to another insurance company, which, in this role, is called the reinsurer . In doing so, the direct... more
The purpose of risk sharing is to spread the risk among those involved. The principal, or direct, insurer may pass on some of the risk to another insurance company, which, in this role, is called the reinsurer . In doing so, the direct insurer is purchasing insurance from the reinsurer. In addition, the direct insurer may structure the policy such that the policyholder – the insured party – is responsible for some of the risk, by including a deductible or policy excess in the conditions of the cover. In this case the insured party has to bear a specified sum whenever a claim is settled – the direct insurer is only responsible for the payment of the amount over and above the excess. The relationship the policyholder has with the direct insurer is parallel to the relationship the direct insurer has with the reinsurer – both the policyholder and the direct insurer are buying insurance to cover part of the risk they are exposed to. Buying insurance protects the policyholder against the effects of “large” losses. Similarly, the inclusion of a reinsurance arrangement often protects the direct insurer against the effects of “very large” claims. In particular it protects the direct insurer against having sole responsibility (or any responsibility) for the tails of the distributions of large claims.
Research Interests: Business and Reinsurance
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Consider an M/G/1 queue with unknown service-time distribution and unknown Poisson arrival rate λ. Given observations of the busy and idle periods of this queue, we construct estimators of λ and of the service-time moment generating... more
Consider an M/G/1 queue with unknown service-time distribution and unknown Poisson arrival rate λ. Given observations of the busy and idle periods of this queue, we construct estimators of λ and of the service-time moment generating function, and we study asymptotic properties of these estimators
Research Interests:
Abstract Focusing on one area of medical concern, blindness, this article serves as a guide for print and electronic resources emphasizing the causes, signs, symptoms, treatment, prognosis, and prevention of specific eye diseases and... more
Abstract Focusing on one area of medical concern, blindness, this article serves as a guide for print and electronic resources emphasizing the causes, signs, symptoms, treatment, prognosis, and prevention of specific eye diseases and disorders. Following a bibliography format, the selected resources include: (1) medical dictionaries, (2) medical and consumer health print resources, (3) medical journals, (4) brochures, (5) professional organizations, and (6) Web sites. This paper concludes with the abbreviated definitions of the predominant eye diseases leading to visual impairment and blindness.
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Gerber and Shiu (1997) have studied the joint density of the time of ruin, the surplus immediately before ruin, and the deficit at ruin in the classical model of collective risk theory. More recently, their results have been generalised... more
Gerber and Shiu (1997) have studied the joint density of the time of ruin, the surplus immediately before ruin, and the deficit at ruin in the classical model of collective risk theory. More recently, their results have been generalised for risk models where the interarrival density for claims is nonexponential, but belongs to the Erlang family. Here we obtain generalisations of the Gerber-Shiu (1997) results that are valid in a general Sparre Andersen model, i.e. for any interclaim density. In particular, we obtain a generalisation of the key formula in that paper. Our results are made more concrete for the case where the distribution between claim arrivals is phase-type or the integrated tail distribution associated with the claim size distribution belongs to the class of subexponential distributions. Furthermore, we obtain conditions for finiteness of the joint moments of the surplus before ruin and the deficit at ruin in the Sparre Andersen model.
Research Interests:
This paper is concerned with optimal strategies for drilling in an oil exploration model. An exploration area containsn1large andn2small oilfields, wheren1andn2are unknown, and represented by a two-dimensional prior distributionπ. A... more
This paper is concerned with optimal strategies for drilling in an oil exploration model. An exploration area containsn1large andn2small oilfields, wheren1andn2are unknown, and represented by a two-dimensional prior distributionπ. A single exploration well discovers at most one oilfield, and the discovery process is governed by some probabilistic law. Drilling a single well costsc, and the values of a large and small oilfield arev1andv2respectively,v1>v2>c>0. At each timet=1,2,…, the operator is faced with the option of stopping drilling and retiring with no reward, or continuing drilling. In the event of drilling, the operator has to choose the numberk,0≤k≤m(mfixed), of wells to be drilled. Rewards are additive and discounted geometrically. Based on the entire history of the process and potentially on future prospects, the operator seeks the optimal strategy for drilling that maximizes the total expected return over the infinite horizon. We show that whenπ≻π′in monotone li...
Research Interests:
Research Interests:
We formulate some general network (and risk) management problems in a Bayesian context, and point out some of the essential features. We argue and demonstrate that, when one is interested in rare events, the Bayesian and frequentist... more
We formulate some general network (and risk) management problems in a Bayesian context, and point out some of the essential features. We argue and demonstrate that, when one is interested in rare events, the Bayesian and frequentist approaches can lead to very different strategies: the former typically leads to strategies which are more conservative. We also present an asymptotic formula
Research Interests: Mathematics, Applied Mathematics, Computer Science, Statistics, Large Deviations, and 12 moreRisk Management, Network Management, Risk theory, Telecommunication Networks, Random Walk, Rare Event, Bayesian decision theory, Bayesian Network, Telecommunication network, Queueing Systems, Numerical Analysis and Computational Mathematics, and Bayesian Probability
Research Interests:
A functional approach is taken for the total claim amount distribution for the individual risk model. Various commonly used approximations for this distribution are considered, including the compound Poisson approximation, the compound... more
A functional approach is taken for the total claim amount distribution for the individual risk model. Various commonly used approximations for this distribution are considered, including the compound Poisson approximation, the compound binomial approximation, the compound negative binomial approximation and the normal approximation. These are shown to arise as zeroth order approximations in the functional set-up. By taking the derivative of the functional that maps the individual claim distributions onto the total claim amount distribution, new first order approximation formulae are obtained as refinements to the existing approximations. For particular choices of input, these new approximations are simple to calculate. Numerical examples, including the well-known Gerber portfolio, are considered. Corresponding approximations for stop-loss premiums are given.
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
In the classical risk model with initial capital u, let τ(u) be the time of ruin, X+(u) be the risk reserve just before ruin, and Y+(u) be the deficit at ruin. Gerber and Shiu (1998) defined the function mδ(u) =E[e−δ τ(u)w(X+(u), Y+(u)) 1... more
In the classical risk model with initial capital u, let τ(u) be the time of ruin, X+(u) be the risk reserve just before ruin, and Y+(u) be the deficit at ruin. Gerber and Shiu (1998) defined the function mδ(u) =E[e−δ τ(u)w(X+(u), Y+(u)) 1 (τ(u) < ∞)], where δ ≥ 0 can be interpreted as a force of interest and w(r,s) as a penalty function, meaning that mδ(u) is the expected discounted penalty payable at ruin. This function is known to satisfy a defective renewal equation, but easy explicit formulae for mδ(u) are only available for certain special cases for the claim size distribution. Approximations thus arise by approximating the desired mδ(u) by that associated with one of these special cases. In this paper a functional approach is taken, giving rise to first-order correction terms for the above approximations.
Research Interests:
Research Interests:
Let ?(u) be the probability of eventual ruin in the classical Sparre Andersen model of risk theory if the initial risk reserve is u. For a large class of such models ?(u) behaves asymptotically like a multiple of exp (–Ru) where R is the... more
Let ?(u) be the probability of eventual ruin in the classical Sparre Andersen model of risk theory if the initial risk reserve is u. For a large class of such models ?(u) behaves asymptotically like a multiple of exp (–Ru) where R is the adjustment coefficient; R depends on the premium income rate, the claim size distribution and the distribution of the time between claim arrivals. Estimation of R has been considered by many authors. In the present paper we deal with confidence bounds for R. A variety of methods is used, including jackknife estimation of asymptotic variances and the bootstrap. We show that, under certain assumptions, these procedures result in interval estimates that have asymptotically the correct coverage probabilities. We also give the results of a simulation study that compares the different techniques in some particular cases.