Within the background field formalism of quantum gravity, I show that if fluctuations are limited to diffeomorphic gauge transformations rather than physical degrees freedom, as in conventional theory, all corrections vanish on shell and effective action is equivalent classical action. In principle, resulting theory finite unitary, requires no renormalization. also this unique parameterization ...

we use the basic binomial option pricing method but allow someor all the parameters in the model to be uncertain and model this uncertaintyusing fuzzy numbers. we show that with the fuzzy model we can, with areasonably small number of steps, consider almost all possible future stockprices; whereas the crisp model can consider only n + 1 prices after n steps.

We prove the existence and uniqueness of fundamental solution for Kolmogorov operators associated to some stochastic processes, that arise in Black & Scholes setting pricing problem relevant path dependent options. improve previous results we provide a closed form expression Cauchy under weak regularity assumptions on coefficients differential operator. Our method is based limiting procedure, w...

We consider a one-dimensional, transient random walk in a random i.i.d. environment. The asymptotic behaviour of such random walk depends to a large extent on a crucial parameter κ > 0 that determines the fluctuations of the process. When 0 < κ < 2, the averaged distributions of the hitting times of the random walk converge to a κ-stable distribution. However, it was shown recently that in this...

A binomial lattice based framework for the analysis of finite investment options with finite operational phase is developed. Solutions for European and American type finite horizon investment options with optimal capital structure and a multi-stage investment setting with multiple debt issues are discussed. The analysis shows that optimal leverage ratios are not affected by option moneyness at ...

Locational marginal pricing (LMP) is a widely employed method for pricing electricity in the wholesale electricity market. Although it is well known that the LMP mechanism is vulnerable to market manipulation, there is little literature providing a systematic analysis of this phenomenon. In the first part of this paper, we investigate the economic dispatch outcomes of the LMP mechanism with str...

In this paper, we present a non-commutative version of some portions of finance theory, including theory of arbitrage, asset princing, and optional decomposition in financial markets based on finite dimensional quantum probability spaces. The binomial model (or, the CRR-model) is studied in the non-commutative setting, and in particular, we prove that a single-step model in non-commutative sett...