Related papers: Probabilistic aspects of finance
In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no arbitrage…
The target of this paper is to consider model the risky asset price on the financial market under the Knightian uncertainty, and pricing the ask and bid prices of the uncertain risk. We use the nonlinear analysis tool, i.e., G-frame work…
This paper presents a stochastic model for discrete-time trading in financial markets where trading costs are given by convex cost functions and portfolios are constrained by convex sets. The model does not assume the existence of a cash…
The pricing and hedging of a general class of options (including American, Bermudan and European options) on multiple assets are studied in the context of currency markets where trading is subject to proportional transaction costs, and…
We study the most famous example of a large financial market: the Arbitrage Pricing Model, where investors can trade in a one-period setting with countably many assets admitting a factor structure. We consider the problem of maximising…
Models necessarily capture only parts of a reality. Prediction models aim at capturing a future reality. In this paper we address the question of how the future is constructed (or: imagined) in an investment context where market…
Modern evolvements of the technologies have been leading to a profound influence on the financial market. The introduction of constituents like Exchange-Traded Funds, and the wide-use of advanced technologies such as algorithmic trading,…
In the paper we study markets with concave transaction costs which depend in a concave way on the volume of transaction. This is typical situation in the case of small investors, which commonly appears in currency and real estate markets.…
We propose a mathematical model of momentum risk-taking, which is essentially real-time risk management focused on short-term volatility of stock markets. Its implementation, our fully automated momentum equity trading system presented…
Recent progress in the development of efficient computational algorithms to price financial derivatives is summarized. A first algorithm is based on a path integral approach to option pricing, while a second algorithm makes use of a neural…
We propose a probabilistic framework for pricing derivatives, which acknowledges that information and beliefs are subjective. Market prices can be translated into implied probabilities. In particular, futures imply returns for these implied…
The problem of hedging and pricing sequences of contingent claims in large financial markets is studied. Connection between asymptotic arbitrage and behavior of the $\alpha$~-~quantile price is shown. The large Black-Scholes model is…
I study the limit of a large random economy, where a set of consumers invests in financial instruments engineered by banks, in order to optimize their future consumption. This exercise shows that, even in the ideal case of perfect…
We present a new approach for studying the problem of optimal hedging of a European option in a finite and complete discrete-time market model. We consider partial hedging strategies that maximize the success probability or minimize the…
We consider arbitrage free valuation of European options in Black-Scholes and Merton markets, where the general structure of the market is known, however the specific parameters are not known. In order to reflect this subjective uncertainty…
We pursue robust approach to pricing and hedging in mathematical finance. We consider a continuous time setting in which some underlying assets and options, with continuous paths, are available for dynamic trading and a further set of…
Three situations in which filtering theory is used in mathematical finance are illustrated at different levels of detail. The three problems originate from the following different works: 1) On estimating the stochastic volatility model from…
One of the shortcomings of the Black and Scholes model on option pricing is the assumption that trading of the underlying asset does not affect the price of that asset. This assumption can be fulfilled only in perfectly liquid markets.…
Prediction markets are often described as mechanisms that ``aggregate information'' into prices, yet the mapping from dispersed private information to observed market histories is typically noisy, endogenous, and shaped by heterogeneous and…
In this review article we explore several recent advances in the quantitative modeling of financial markets. We begin with the Efficient Markets Hypothesis and describe how this controversial idea has stimulated a number of new directions…