相关论文: A general methodology to price and hedge derivativ…
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…
A derivative is a financial security whose value is a function of underlying traded assets and market outcomes. Pricing a financial derivative involves setting up a market model, finding a martingale (``fair game") probability measure for…
We use a continuous version of the standard deviation premium principle for pricing in incomplete equity markets by assuming that the investor issuing an unhedgeable derivative security requires compensation for this risk in the form of a…
Expanding the ideas of the author's paper 'Nonexpansive maps and option pricing theory' (Kibernetica 34:6 (1998), 713-724) we develop a pure game-theoretic approach to option pricing, by-passing stochastic modeling. Risk neutral…
In common finance literature, Black-Scholes partial differential equation of option pricing is usually derived with no-arbitrage principle. Considering an asset market, Merton applied the Hamilton-Jacobi-Bellman techniques of his…
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 propose a deep learning approach to study the minimal variance pricing and hedging problem in an incomplete jump diffusion market. It is based upon a rigorous stochastic calculus derivation of the optimal hedging portfolio, optimal…
Risk-neutral pricing dictates that the discounted derivative price is a martingale in a measure equivalent to the economic measure. The residual ambiguity for incomplete markets is here resolved by minimising the entropy of the price…
In this paper we provide a quantitative analysis to the concept of arbitrage, that allows to deal with model uncertainty without imposing the no-arbitrage condition. In markets that admit ``small arbitrage", we can still make sense of the…
The objective of this paper is to provide a comprehensive study no-arbitrage pricing of financial derivatives in the presence of funding costs, the counterparty credit risk and market frictions affecting the trading mechanism, such as…
As operators acting on the undetermined final settlement of a derivative security, expectation is linear but price is non-linear. When the market of underlying securities is incomplete, non-linearity emerges from the bid-offer around the…
The problem of determining the European-style option price in the incomplete market has been examined within the framework of stochastic optimization. An analytic method based on the discrete dynamic programming equation (Bellman equation)…
With model uncertainty characterized by a convex, possibly non-dominated set of probability measures, the agent minimizes the cost of hedging a path dependent contingent claim with given expected success ratio, in a discrete-time,…
This article presents a deep reinforcement learning approach to price and hedge financial derivatives. This approach extends the work of Guo and Zhu (2017) who recently introduced the equal risk pricing framework, where the price of a…
We consider a nondominated model of a discrete-time financial market where stocks are traded dynamically, and options are available for static hedging. In a general measure-theoretic setting, we show that absence of arbitrage in a…
A common assumption in financial engineering is that the market price for any derivative coincides with an objectively defined risk-neutral price - a plausible assumption only if traders collectively possess objective knowledge about the…
We formalize in the proof assistant Isabelle essential basic notions and results in financial mathematics. We provide generic formal definitions of concepts such as markets, portfolios, derivative products, arbitrages or fair prices, and we…
The classical discrete time model of proportional transaction costs relies on the assumption that a feasible portfolio process has solvent increments at each step. We extend this setting in two directions, allowing for convex transaction…
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…
We develop two alternate approaches to arbitrage-free, market-complete, option pricing. The first approach requires no riskless asset. We develop the general framework for this approach and illustrate it with two specific examples. The…