Journal of Computational and Applied Mathematics, 1995
When limited information on the distribution of a positive random variable X (continuous or discr... more When limited information on the distribution of a positive random variable X (continuous or discrete) is known (e.g., mode, mean, variance), the tail probability P(X⩾t) cannot be chosen independently. In this paper supremum and infimum for P(X⩾t) will be calculated over the set of positive random variables with unique mode, mean and/or variance given.
When limited information on the distribution of a positive random variable X (continuous or discr... more When limited information on the distribution of a positive random variable X (continuous or discrete) is known (e.g., mode, mean, variance), the tail probability P(X⩾t) cannot be chosen independently. In this paper supremum and infimum for P(X⩾t) will be calculated over the set of positive random variables with unique mode, mean and/or variance given.
Abstract By means of Wiener processes, randomness in interest rates for annuities can be modelled... more Abstract By means of Wiener processes, randomness in interest rates for annuities can be modelled. This paper wants to give an expression for the Laplace transform of annuities certain, when time is exponentially distributed.
... A. DE SCHEPPER, MJ GOOVAERTS and R. KAAS De Schepper A, Goovaerts MJ, Kaas R. A recursive sch... more ... A. DE SCHEPPER, MJ GOOVAERTS and R. KAAS De Schepper A, Goovaerts MJ, Kaas R. A recursive scheme for perpetu-ities with random positive interest rates. Part I. Analytical results. Scand. ... 10, 275-287. De Schepper, A., De Vylder, F., Goovaerts. M. & Kaas, R. (l992a). ...
Common interest rate models are faced with the problem of volatilities vanishing for spot rates i... more Common interest rate models are faced with the problem of volatilities vanishing for spot rates in the vicinity of zero. A possible answer to this difficulty can be given by the introduction of a reflecting boundary at zero, at the same time guaranteeing the spot rate to be non-negative, which is needed in order to avoid the possibility of arbitrage. In the present paper, we obtain closed form expressions for transition probabilities and for prices of general interest rate contingent claims by means of path integrals, when the spot rate process is modelled by means of a general diffusion with a reflecting or absorbing boundary. We also show how to derive accurate closed form approximations in case the path integrals are not analytically computable.
In this paper, we apply the results about d and d-function perturbations in order to formulate wi... more In this paper, we apply the results about d and d-function perturbations in order to formulate within the Feynman-Kac integration the solution of the forward Fokker-Planck equation subject to Dirichlet or Neumann boundary conditions. We introduce the concept of convex order to derive upper and lower bounds for path integrals with d and d- functions in the integrand. We suggest the use of bounds as an approximation for the solution.
Journal of Computational and Applied Mathematics, 1995
When limited information on the distribution of a positive random variable X (continuous or discr... more When limited information on the distribution of a positive random variable X (continuous or discrete) is known (e.g., mode, mean, variance), the tail probability P(X⩾t) cannot be chosen independently. In this paper supremum and infimum for P(X⩾t) will be calculated over the set of positive random variables with unique mode, mean and/or variance given.
When limited information on the distribution of a positive random variable X (continuous or discr... more When limited information on the distribution of a positive random variable X (continuous or discrete) is known (e.g., mode, mean, variance), the tail probability P(X⩾t) cannot be chosen independently. In this paper supremum and infimum for P(X⩾t) will be calculated over the set of positive random variables with unique mode, mean and/or variance given.
Abstract By means of Wiener processes, randomness in interest rates for annuities can be modelled... more Abstract By means of Wiener processes, randomness in interest rates for annuities can be modelled. This paper wants to give an expression for the Laplace transform of annuities certain, when time is exponentially distributed.
... A. DE SCHEPPER, MJ GOOVAERTS and R. KAAS De Schepper A, Goovaerts MJ, Kaas R. A recursive sch... more ... A. DE SCHEPPER, MJ GOOVAERTS and R. KAAS De Schepper A, Goovaerts MJ, Kaas R. A recursive scheme for perpetu-ities with random positive interest rates. Part I. Analytical results. Scand. ... 10, 275-287. De Schepper, A., De Vylder, F., Goovaerts. M. & Kaas, R. (l992a). ...
Common interest rate models are faced with the problem of volatilities vanishing for spot rates i... more Common interest rate models are faced with the problem of volatilities vanishing for spot rates in the vicinity of zero. A possible answer to this difficulty can be given by the introduction of a reflecting boundary at zero, at the same time guaranteeing the spot rate to be non-negative, which is needed in order to avoid the possibility of arbitrage. In the present paper, we obtain closed form expressions for transition probabilities and for prices of general interest rate contingent claims by means of path integrals, when the spot rate process is modelled by means of a general diffusion with a reflecting or absorbing boundary. We also show how to derive accurate closed form approximations in case the path integrals are not analytically computable.
In this paper, we apply the results about d and d-function perturbations in order to formulate wi... more In this paper, we apply the results about d and d-function perturbations in order to formulate within the Feynman-Kac integration the solution of the forward Fokker-Planck equation subject to Dirichlet or Neumann boundary conditions. We introduce the concept of convex order to derive upper and lower bounds for path integrals with d and d- functions in the integrand. We suggest the use of bounds as an approximation for the solution.
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