The problems inherent in expert systems which model human design processes are discussed. An exam... 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.
We consider the classical risk model where claims X1, X2, . . . arrive in a compound Poisson proc... 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
The purpose of risk sharing is to spread the risk among those involved. The principal, or 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.
Communications in Statistics. Stochastic Models, 1999
Consider an M/G/1 queue with unknown service-time distribution and unknown Poisson arrival rate λ... 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
Abstract Focusing on one area of medical concern, blindness, this article serves as a guide for p... 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.
Gerber and Shiu (1997) have studied the joint density of the time of ruin, the surplus immediatel... 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.
Journal of Applied Mathematics and Stochastic Analysis, 2005
This paper is concerned with optimal strategies for drilling in an oil exploration model. An expl... 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...
The problems inherent in expert systems which model human design processes are discussed. An exam... 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.
We consider the classical risk model where claims X1, X2, . . . arrive in a compound Poisson proc... 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
The purpose of risk sharing is to spread the risk among those involved. The principal, or 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.
Communications in Statistics. Stochastic Models, 1999
Consider an M/G/1 queue with unknown service-time distribution and unknown Poisson arrival rate λ... 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
Abstract Focusing on one area of medical concern, blindness, this article serves as a guide for p... 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.
Gerber and Shiu (1997) have studied the joint density of the time of ruin, the surplus immediatel... 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.
Journal of Applied Mathematics and Stochastic Analysis, 2005
This paper is concerned with optimal strategies for drilling in an oil exploration model. An expl... 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...
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