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Estimation of the covariance matrix of asset returns from high frequency data is complicated by asynchronous returns, market mi- crostructure noise and jumps. One technique for addressing both asynchronous returns and market microstructure…
We find the variance-optimal equivalent martingale measure when multivariate assets are modeled by a regime-switching geometric Brownian motion, and the regimes are represented by a homogeneous continuous time Markov chain. Under this new…
We present a framework for hedging a portfolio of derivatives in the presence of market frictions such as transaction costs, market impact, liquidity constraints or risk limits using modern deep reinforcement machine learning methods. We…
Automated market makers (AMMs) are pricing mechanisms utilized by decentralized exchanges (DEX). Traditional AMM approaches are constrained by pricing solely based on their own liquidity pool, without consideration of external markets or…
In this paper, we consider the problem of equal risk pricing and hedging in which the fair price of an option is the price that exposes both sides of the contract to the same level of risk. Focusing for the first time on the context where…
In this article we consider an optimization problem of expected utility maximization of continuous-time trading in a financial market. This trading is constrained by a benchmark for a utility-based shortfall risk measure. The market…
We study the valuation and hedging problem of European options in a market subject to liquidity shocks. Working within a Markovian regime-switching setting, we model illiquidity as the inability to trade. To isolate the impact of such…
The aim of this paper is to solve an optimal investment, consumption and life insurance problem when the investor is restricted to capital guarantee. We consider an incomplete market described by a jump-diffusion model with stochastic…
Modelling stock prices via jump processes is common in financial markets. In practice, to hedge a contingent claim one typically uses the so-called delta-hedging strategy. This strategy stems from the Black--Merton--Scholes model where it…
This paper considers options pricing when the assumption of normality is replaced with that of the symmetry of the underlying distribution. Such a market affords many equivalent martingale measures (EMM). However we argue (as in the…
We consider derivatives written on multiple underlyings in a one-period financial market, and we are interested in the computation of model-free upper and lower bounds for their arbitrage-free prices. We work in a completely realistic…
We suggest a simple reduction of pricing European options in affine jump-diffusion models to pricing options with modified payoffs in diffusion models. The procedure is based on the conjugation of the infinitesimal generator of the model…
We study a financial market where the risky asset is modelled by a geometric It\^o-L\'{e}vy process, with a singular drift term. This can for example model a situation where the asset price is partially controlled by a company which…
We consider the pricing of derivatives in a setting with trading restrictions, but without any probabilistic assumptions on the underlying model, in discrete and continuous time. In particular, we assume that European put or call options…
We introduce a criterion how to price derivatives in incomplete markets, based on the theory of growth optimal strategy in repeated multiplicative games. We present reasons why these growth-optimal strategies should be particularly relevant…
The linear Fisher market (LFM) is a basic equilibrium model from economics, which also has applications in fair and efficient resource allocation. First-price pacing equilibrium (FPPE) is a model capturing budget-management mechanisms in…
Discrete diffusion models (DDMs) are a powerful class of generative models for categorical data, but they typically require many function evaluations for a single sample, making inference expensive. Existing acceleration methods either rely…
We propose methods to infer jumps of a semi-martingale, which describes long-term price dynamics, based on discrete, noisy, high-frequency observations. Different to the classical model of additive, centered market microstructure noise, we…
The general method is proposed for constructing a family of martingale measures for a wide class of evolution of risky assets. The sufficient conditions are formulated for the evolution of risky assets under which the family of equivalent…
This paper studies the topic of cost-efficiency in incomplete markets. A payoff is called cost-efficient if it achieves a given probability distribution at some given investment horizon with a minimum initial budget. Extensive literature…