In Kusuda [45], we developed equilibrium analysis in security market economy with jump-Wiener information where no finite number of securities can complete markets. Assuming approximately complete markets (Björk et al. [11] [12]) in which a continuum of bonds are traded and any contingent claim...

We provide results on the existence and uniqueness of equilibrium in dynamically incomplete financial markets in discrete time. Our framework allows for heterogeneous agents, unspanned random endowments and convex trading constraints. In the special case where all agents have preferences of the...

We consider a full equilibrium model in continuous time comprising a finite number of agents and tradable securities.We show that, if the agents' endowments are spanned by the securities and if the agents have entropic utilities, an equilibrium exists and the agents' optimal trading strategies...

Classical quantitative finance models such as the Geometric Brownian Motion or its later extensions such as local or stochastic volatility models do not make sense when seen from a physics-based perspective, as they are all equivalent to a negative mass oscillator with a noise. This paper...

A new acceptable price approach to stochastic endpoint determination at given horizon accounting for the marginal investor beliefs and behaviour was proposed. Two-sided filtration with FBSDE defined stochastic dynamics was formulated for acceptable asset price under the risk-neutral probability...

In this paper, we combine the theory of stochastic process and techniques of machine learning with the regression analysis, first proposed by Longstaff and Schwartz 2001 and apply the new methodologies on financial derivatives pricing. Rigorous convergence proofs are provided for some of the...

We develop a mathematical proof demonstrating that only financially-strong firms will sell put options on their own stock, but financially-weak firms will not. The sale of options on a company's own stock exposes the buyer to default risk of the issuer, which additionally complicates the payoff...

This manuscript reviews standard classes of Libor Market models and discusses their numerical approximation machinery. It gives introduction to non-defaultable, defaultable models, Levy-forced models and affine Libor models

Measuring the performance of stock portfolios that include options is challenging due to options' nonlinearity in the underlying, their exposure to volatility risk, and their time decay. Our contribution to the literature is twofold: First, we provide a theoretically rigorous derivation of the...