Advances in Stochastic Modelling and Data Analysis by Jacques Janssen (auth.), Jacques Janssen, Christos H.

By Jacques Janssen (auth.), Jacques Janssen, Christos H. Skiadas, Constantin Zopounidis (eds.)

Advances in Stochastic Modelling and information Analysis offers the latest advancements within the box, including their purposes, in most cases within the parts of assurance, finance, forecasting and advertising and marketing. additionally, the prospective interactions among information research, man made intelligence, choice aid structures and multicriteria research are tested via most sensible researchers.
Audience: a large readership drawn from theoretical and utilized mathematicians, resembling operations researchers, administration scientists, statisticians, machine scientists, bankers, advertising managers, forecasters, and medical societies corresponding to EURO and TIMS.

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This issue can be rephrased in sharper, analytic terms as: how much time will elapse, on average, before the gambler's discounted net gain reaches a boundary level of zero? In Section 2 we demonstrate the relative ease with which one can derive--via martingale methods--the Laplace transform of the first passage time (to a single boundary) density function of a Brownian motion with drift. The derivation begins with a straightforward application of the optional sampling theorem to martingales associated 32 with Brownian motion.

LkO and v>O. (A31) Thus, whenever v and B have different signs, the density ofT8 under p is defective since T0 is infinite with positive probability. B and v have different signs or v:s;O. • Note, for a slightly different starting point in the proof, the reader is urged to consult Karatzas and Shreve (1991, pp. 196-197). O, we obtain E[T0] = B/v, where B,v>O. • 54 REFERENCES 1. N. and E. C. Waymire. Stochastic Processes With Applications, Wiley, New York, 1990. 2. Chernoff, H. 'Sequential Tests For the Mean of a Normal Distribution', in: Pro c.

The first lemma specifies the relationship between the stock price at time zero and the optimal exercise price S* that excludes the possibility of a zero exercise time; an uninteresting case. 1: Suppose that there exists a solution to the option holder's optimal exercise (stopping) problem. If S(O) 0. 1. 2: The Laplace transform ofT6 is: The third lemma specifies the relationship that must hold between the parameters 13 and v (as well as the sign of v), for the exercise time to be finite-valued with probability one.

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