Optimal option pricing and trading: a new theory

We introduce a new utility-based approach to pricing European and American options. In so doing, we overcome some of the limitations of the existing models.option, derivative, asset, stochastic

The theory of the firm under multiple uncertainties

Without imposing restrictions on the utility function and the probability distributions, we show the impact of multiple uncertainty (and each single uncertainty) and change in risk aversion on each input demand. In so doing, we emphasize the importance of the relationship between the inputs in this impact. Moreover, the paper provides technical contributions.uncertainty, firm

Estimation with price and output uncertainty

This paper extends the existing estimation methods to allow estimation under simultaneous price and output uncertainty. In contrast with the previous literature, our approach is applicable to the direct and indirect utility functions and does not require specification and estimation of the production function. We derive estimating equations for the two most common forms of output risk (additive and multiplicative risks) and empirically determine which form is appropriate. Moreover, our estimation method can be utilized by future empirical studies in several ways. First, our method can be extended to include multiple sources of uncertainty. Second, it is applicable to other specifications of output uncertainty. Third, it can be used to conduct hypothesis tests regarding the functional forms and distributions. Furthermore, it enables the future empirical researcher to empirically verify/ refute the theoretical comparative statics results.estimating equations, output uncertainty, price uncertainty, utility

General Smooth Solutions to the HJB PDE: Applications to Finance

We overcome a major obstacle in mathematical optimization. In so doing, we provide a smooth solution to the HJB PDE without assuming the differentiability of the value function. We apply our method to financial models

Adding one risk to another: generalizing the unavoidable (background) risk

ResumenEste artículo ofrece una generalización del modelo de riezgo subyacente. En primer lugar, se relajan los supuestos de independencia. En segundo lugar, se adopta una forma funcional general. Tercero, se adopta un tipo de riesgo general. Adicionalmente se presenta una nueva forma general de riesgo subyacente.AbstractThis paper provides a complete generalization of the background risk models. In so doing, first, it relaxes the independence assumption. Second, it adopts a general functional form. Third, it adopts a general type of risk. Furthermore, it introduces a new general form of background risk.Background risk, uncertainty

Theory of the firm under multiple uncertainties

Without imposing restrictions on the utility function and the probability distributions, we show the impact of multiple uncertainty (and each single uncertainty) and change in risk aversion on each input demand. In so doing, we emphasize the importance of the relationship between the inputs in this impact. Moreover, the paper provides technical contributions.firm, uncertainty, risk, production

The distribution of the average of log-normal variables and exact Pricing of the Arithmetic Asian Options: A Simple, closed-form Formula

We overcome a long-standing obstacle in statistics. In doing so, we show that the distribution of the sum of log-normal variables is log-normal. Furthermore, we offer a breakthrough result in finance. In doing so, we introduce a simple, exact and explicit formula for pricing the arithmetic Asian options. The pricing formula is as simple as the classical Black-Scholes formula

A new approach to stochastic optimization: the investment-consumption model

We derive general explicit solutions to the investment-consumption model without the restrictive assumption of HARA or exponential utility function and without reliance on the existing duality or variational methods.portfolio, investment, stochastic optimization

New developments in econophysics: Option pricing formulas

We synthesize and discuss some new developments in econophysics. In doing so, we focus on option pricing. We relax the assumptions of constant volatility and interest rate. In doing so, we rely on the square root of the Brownian motion. We also provide simple, closed-form pricing formulas for the American and Bermudan options.Comment: This article is published in a journa