We propose a discrete time algorithm for the valuation of employee stock options based on exponential indifference prices and taking into account both the possibility of partial exercise of aâ€¦ (More)

It is well documented that executives granted stock options tend to exercise early and in a few large transactions or â€˜blocksâ€™. Standard risk-neutral valuation models cannot explain these patterns,â€¦ (More)

In this paper we recast the Coxâ€“Ingersollâ€“Ross model of interest rates into the chaotic representation recently introduced by Hughston and Rafailidis. Beginning with the â€œsquared Gaussianâ€¦ (More)

We apply a utilityâ€“based method to obtain the value of a finiteâ€“time investment opportunity when the underlying real asset is not perfectly correlated to a traded financial asset. Using aâ€¦ (More)

We show that, in finite dimensions, the only monotone metrics on the space of invertible density matrices for which the (+1) and (âˆ’1) affine connections are mutually dual are constant multiples ofâ€¦ (More)

We show how to obtain the mixture connection in an infinite dimensional information manifold and prove that it is dual to the exponential connection with respect to the Fisher information. We alsoâ€¦ (More)

Let H0 â‰¥ I be a self-adjoint operator and let V be a form-small perturbation such that âˆ¥âˆ¥R 1 2 +Îµ 0 V R 1 2 âˆ’Îµ 0 âˆ¥âˆ¥ < âˆž, where Îµ âˆˆ (0, 1/2) and R0 = H 0 . Suppose that there exists a positive Î² < 1â€¦ (More)

We apply the concepts of utility based pricing and hedging of derivatives in stochastic volatility markets and introduce a new class of " reciprocal affine " models for which the indifference priceâ€¦ (More)

In this paper we recast the Coxâ€“Ingersollâ€“Ross model of interest rates into the chaotic representation recently introduced by Hughston and Rafailidis. Beginning with the â€œsquared Gaussianâ€¦ (More)

Insurance companies often include very long-term guarantees in participating life insurance products, which can turn out to be very valuable. Under a guaranteed annuity options (g.a.o.), the insurerâ€¦ (More)