xVA is a collection of valuation adjustments made to the classical risk-neutral valuation of a derivative or derivatives portfolio for pricing or for accounting purposes, and it has been a matter of debate and controversy. This presentation is intended to clarify the notion of xVA as well as the usage of the xVA items in…
A commonly used stochastic model for the derivative and commodity market analysis is the Barndorff-Nielsen and Shephard (BN-S) model. At first, an application of the BN-S model will be presented to find an optimal hedging strategy for the oil commodity from the Bakken, a new region of oil extraction that is benefiting from fracking technology.…
Motivated by modeling borrowing and lending between banks, we start by illustrating systemic risk with a toy model of diffusions processes coupled through their drifts. We then show that such a simplistic model is in fact a Nash equilibrium of a Linear-Quadratic differential game. In order to take into account clearing debt obligations a delay…
We present a new combined Mean Field Control Game (MFCG) problem which can be interpreted as a competitive game between collaborating groups and its solution as a Nash equilibrium between the groups. Within each group the players coordinate their strategies. An example of such a situation is a modification of the classical trader's problem. Groups…
This article is about yield farming, which refers to a decentralized finance strategy of providing liquidity and seeking associated rewards in the form of transpired-transaction fees. We explain and demystify yield farming and quantify transaction costs, returns, and risks using on-chain data from major decentralized exchanges. We provide a mathematical framework that resembles a representative…
We study Merton’s expected utility maximization problem in an incomplete market, characterized by a factor process in addition to the stock price process, where all the model primitives are unknown. We take the reinforcement learning (RL) approach to learn optimal portfolio policies directly by exploring the unknown market, without attempting to estimate the model parameters.…