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

*Advances in Stochastic Modelling and information Analysis* offers the newest advancements within the box, including their purposes, commonly within the parts of coverage, finance, forecasting and advertising. additionally, the potential interactions among facts research, synthetic intelligence, selection aid platforms and multicriteria research are tested by means of most sensible researchers. *Audience:* a large readership drawn from theoretical and utilized mathematicians, similar to operations researchers, administration scientists, statisticians, desktop scientists, bankers, advertising managers, forecasters, and clinical societies reminiscent of EURO and TIMS.

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Lj B(O). 22). 5. CONCLUSION This paper shows the possibility to analyze the dynamic evolution of a segmented balance sheet on basis of our preceding models, extending Merton's (1990) ideas. Moreover, we present a first connection with classical portfolio theory but in continuous time. The new concept of CALM gives a measure of danger for the company and the classical notion of duration can be extended for a measure of mean immunization. This last extension gives the possibility to define new matching constraints that could be added to the mathematical programming to be solved for finding the optimal portfolio at time t.

The First Passage Density of a Continuous Gaussian Process to a General Boundary', J. Appl. Prob. 22, 99-122 (1985). 6. Durbin, J. and D. Williams. 'The First-Passage Density of the Brownian Motion to a Curved Boundary', J. Appl. Prob. 29, 291-304 (1992). 7. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. , Wiley, New York, 1968. 55 8. Garman, M. 'Semper Tempus Fugit', RISK, 2, 5:34-35 (1989). 9. V. 'On Transforming a Certain Class of Stochastic Processes by Absolutely Continuous Substitution of Measures,' Theory Probab.

Finally, the third asset is a perpetual American call option with an exercise price, q=$1. 1. Results In this context McKean obtained a closed-form solution for the two unknowns of the warrant holder's valuation (optimal stopping) problem. 4) =r - p. 2. Replication in Karatzas' Framework Replicating McKean's result in Karatzas' framework is not straightforward. As Karatzas (1988, p. 54) indicates, to evaluate perpetual options two technical difficulties have to be surmounted. That is, W(t) must now be: i) a Brownian motion on the entire set [O,oo], and ii) accompanied by a filtration that measures all of the processes in the model.