PARAMETRIC ESTIMATION OF DIFFUSION PROCESSES SAMPLED AT FIRST EXIT TIME

This paper introduces a family of recursively defined estimators of the parameters of a diffusion process. We use ideas of stochastic algorithms for the construction of the estimators. Asymptotic consistency of these estimators and asymptotic normality of an appropriate normalization are proved. The results are applied to two examples from the financial literature; viz., Cox-Ingersoll-Ross' model and the constant elasticity of variance (CEV) process illustrate the use of the technique proposed herein.Continuous time Markov processes, discrete time sampling, diffusions, interest rate models, stochastic algorithms.

State Tameness: A New Approach for Credit Constrains

We propose a new definition for tameness within the model of security prices as It\^o processes that is risk-aware. We give a new definition for arbitrage and characterize it. We then prove a theorem that can be seen as an extension of the second fundamental theorem of asset pricing, and a theorem for valuation of contingent claims of the American type. The valuation of European contingent claims and American contingent claims that we obtain does not require the full range of the volatility matrix. The technique used to prove the theorem on valuation of American contingent claims does not depend on the Doob-Meyer decomposition of super-martingales; its proof is constructive and suggest and alternative way to find approximations of stopping times that are close to optimal.arbitrage, pricing of contingent claims, continuous-time financial markets, tameness

Hodge-Deligne polynomials of character varieties of abelian groups

Let F be a finite group and X be a complex quasi-projective F-variety. For r in N, we consider the mixed Hodge-Deligne polynomials of quotients X^r/F, where F acts diagonally, and compute them for certain classes of varieties X with simple mixed Hodge structures. A particularly interesting case is when X is the maximal torus of an affine reductive group G, and F is its Weyl group. As an application, we obtain explicit formulae for the Hodge-Deligne and E-polynomials of (the distinguished component of) G-character varieties of free abelian groups. In the cases G=GL(n,C) and SL(n,C) we get even more concrete expressions for these polynomials, using the combinatorics of partitions.Comment: Rephrased some results in section 5 (in particular, Lemma 5.5 was corrected, and Remark 5.6 added); other minor improvement