Economics - Research Publications

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    Bounded rationality: static versus dynamic approach
    Basov, S. ( 2002-12)
    Two kinds of theories of the boundedly rational behavior are possible. Static theories focus on stationary behavior and do not include any explicit mechanism for temporal change. Dynamic theories, on the other hand, explicitly model the fine-grain adjustments made by the subjects in response to their recent experiences. The main contribution of this paper is to argue that the restrictions usually imposed on the distribution of choices in the static approach are generically not supported by an explicit adjustment mechanism
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    A partial characterization of the solution of the multidimensional screening problem with nonlinear preferences
    Basov, S. ( 2002-11)
    In this paper I apply the Hamiltonian method to solve the relaxed multidimensional screening problem. I also illustrate by some examples that the Hamiltonian technique coupled with implementability criterion developed by Carlier [2002] sometimes allows us to arrive at a complete solution of a screening problem.
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    A general class of risk models
    DUFRESNE, DANIEL ( 2002-01)
    We consider the actuarial risk model when the waiting times or claims have a Laplace transform which is a rational function. This generalizes the classical model, where the waiting times are expotenial, and give more flexibility in the modelling of a risk business. Ruin is seen as a random walk crossing a barrier; the summands of the random walk are expressed as the difference of the waiting time and the claim. The class R of distributions which have finite Laplace transforms includes the so-called phase-type distributions. For waiting times in R , the Laplace transform of the ruin probability is obtained explicitly; if the calims are in R , then the probability of ruin is a combination of exponentials times polynomials, which can be found in closed-form.
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    The Gerber-Shiu discounted penalty function in the stationary renewal risk model
    Willmot, Gordon E. ; Dickson, David C. M. ( 2002-08)
    The discounted penalty function introduced by Gerber and Shiu (1998) is considered in the stationary renewal risk model, where it is expressed in terms of the same discounted penalty function in the ordinary renewal risk model. This relationship unifies and generalizes known special cases. An invariance property between the stationary renewal risk model and the classical Poisson model with respect to the ruin probability is also generalized as a result.
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    The integrated square-root process
    DUFRESNE, DANIEL ( 2001-11)
    The square-root process has been used to model interest rates and stochastic volatility. This paper studies some of its properties, particularly those of the integral of the process over time. After summarizing the properties of the square-root process, the Laplace transform of the integral of the square-root process is derived. Three methods for the computation of the moments of this integral are given, as well as some properties of the density of the integral. The last section studies the relationship between the Laplace transforms of a variable and of its reciprocal, a topic which arises in the previous analysis and elsewhere. An application to the generalized inverse Gaussian distribution is given
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    On the expected discounted penalty function at ruin of a surplus process with interest
    Cai, Jun ; Dickson, David C.M. ( 2001-11)
    In this paper, we study the expected value of a discounted penalty function at ruin of the classical surplus process modified by the inclusion of interest of the surplus. The 'penalty' is simply a function of the surplus immediately prior to ruin and the deficit at ruin. An integral equation for the expected value is derived, while the exact solution is given when the initial surplus is zero. Dickson's (1992) formulae for the distribution of the surplus immediately prior to ruin in the classical surplus process are generalised to our modified surplus process.
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    Asian and Basket Asymptotics
    DUFRESNE, DANIEL ( 2002-07)
    The pricing of Asian or basket options is directly related to finding the distributions of sums of lognormal random variables. There is no general explicit formula for those distributions. This paper looks at the limit distributions of sums of lognormal variables when volatility, or maturity, tends to either 0 or to infinity. The limits obtained are either normal or lognormal, depending on the normalization chosen. This justifies the lognormal approximation, much used in practice, and also gives an asymptotically exact distribution for averages of lognormals with a relatively small volatility; it has been noted that all the analytical pricing formulas for Asian options perform poorly for small volatilities. Asymptotic formulas are also found for the moments of the sums of lognormals. Results are given for both discrete and continuous averages.
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    Ruin Probabilities with a Markov Chain Interest Model
    Cai, Jun ; Dickson, David C. M. ( 2002-08)
    Ruin probabilities in two generalized discrete time risk processes with a Markov chain interest model are studied. Recursive and integrat equations for the ruin probabilities are given. Generalized Lundberg inequalities for the ruin probabilities are derived both by inductive and martingale approaches. The relationships between these inequalities are discussed. A numerical example is given to illustrate these results.
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    A Gibbs' Sampler for the Parameters of a Truncated Multivariate Normal Distribution
    GRIFFITHS, WILLIAM ( 2002-09)
    The inverse distribution function method for drawing randomly from normal andtruncated normal distributions is used to set up a Gibbs' sampler for the posterior densityfunction of the parameters of a truncated multivariate normal distribution. The sampler isapplied to shire level rainfall for five shires in Western Australia.
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    Further Observations on Chain Ladder Bias
    Taylor, Greg ( 2002-01)
    The chain ladder forecast (CLF) has previously been shown to be biased upward. The present paper calculates the second order approximation to the magnitude of the bias, ie the Taylor series for the bias truncated at terms involving second order moments of observations. Some order relations between data triangles are obtained with respect to this second order bias. While the prediction error of the CLF, as a predictor of loss reserve, does not have zero mean, it does have zero median under certain circumstances. Some numerical consequences are explored.