By Jacques Janssen (auth.), Jacques Janssen, Christos H. Skiadas, Constantin Zopounidis (eds.)
Advances in Stochastic Modelling and knowledge Analysis offers the newest advancements within the box, including their functions, as a rule within the components of assurance, finance, forecasting and advertising. additionally, the potential interactions among information research, man made intelligence, choice help structures and multicriteria research are tested by means of best researchers.
Audience: a large readership drawn from theoretical and utilized mathematicians, equivalent to operations researchers, administration scientists, statisticians, laptop scientists, bankers, advertising managers, forecasters, and medical societies reminiscent of EURO and TIMS.
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National Science Foundation. 29 J. Jansen et al. ), Advances in Stochastic Modelling and Data Analysis, 29-56. @ 1995 Kluwer Academic Publishers. 30 Expected Optimal Exercise Time of a Perpetual American Option: A Closed-form Solution ABSTRACT Using martingale methods, we find that the expected optimal exercise time of a perpetual, dividend-paying American call option contract is: the ratio of the time-independent stopping boundary to the risk-adjusted drift of the stock price process. This ratio is an analytical expression.
Of course, these densities would, subsequently be integrated in order to compute the moments. Likewise, the mean (and higher moments) for processes other than Brownian motion with drift should also be computed via martingale methods. Then, a basis would exist for comparing the computational effort of this work against the results of Ricciardi and Sato (1988). 45 They have derived closed-form expressions for all moments of the first passage time of the unrestricted, conditional Omstein-Uhlenbeck process with a constant boundary.
Thus, permitting a unified approach to the problems of: option pricing, consumption and investment, and equilibrium in a financial market. Our main financial result is that (for a perpetual, dividendpaying American call option) the optimal exercise time is the ratio of the stopping boundary (b) to the drift of the transformed stock price process. Here, b equals the product of the inverse of the stock volatility times the log of the ratio of the optimal exercise stock price to the initial (time zero) stock price.