Motivated by the Kyle-Back model of 'insider trading', we consider certain classes of linear transformations of two independent Brownian motions and study their canonical decomposition as semimartingales in their own filtration. In particular we characterize those transformations which generate...

We show the existence, for any k E N, of processes which have the same k-marginals as Brownian motion, although they are not Brownian motions. For k = 4, this proves a conjecture of Stoyanov. The law P' of such a weak Brownian motion of order k can be constructed to be equivalent to Wiener...

Diffusions are widely used in finance due to their tractability. Driftless diffusions are needed to describe ratios of asset prices under a martingale measure. We provide a simple example of a tractable driftless diffusion which also has a bounded state space.

The Cox, Ross, and Rubinstein binomial model is generalized to the multinomial case. Limits are investigated and shown to yield the Black-Scholes formula in the case of continuous sample paths for a wide variety of complete market structures. In the discontinuous case a Merton-type formula is...

Investors in equilibrium are modeled as facing investor specific risks across the space of assets. Personalized asset pricing models reflect these risks. Averaging across the pool of investors we obtain a market asset pricing model that reflects market risk exposures. It is observed on invoking...

Contingent claims with payoffs depending on finitely many asset prices are modeled as elements of a separable Hilbert space. Under fairly general conditions, including market completeness, it is shown that one may change measure to a reference measure under which asset prices are Gaussian and...

European call options are priced when the uncertainty driving the stock price follows the V. G. stochastic process (Madan and Seneta 1990). The incomplete markets equilibrium change of measure is approximated and identified using the log return mean. variance, and kurtosis. An exact equilibrium...

This paper expands and tests the approach of Madan and Milne (1994) for pricing contingent claims as elements of a separable Hilbert space. We specialize the Hilbert space basis to the family of Hermite polynomials and use the model to price options on Eurodollar futures. Restrictions on the...

This paper tests the approach of Madan and Milne (1994) and its extension in Abken, Madan, and Ramamurtie (1996) for pricing contingent claims as elements of a separable Hilbert space. We specialize the Hilbert space basis to the family of Hermite polynomials and test the model on S&P 500 index...

Investors in equilibrium are modeled as facing investor specific risk exposures arising from incomplete diversification of personal risks across the space of assets. Personalized asset pricing models reflect these risks. Averaging across the pool of investors we obtain a market asset pricing...