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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…
The objective of the paper is to price weather contracts using temperature as the underlying process when the later follows a mean-reverting dynamics driven by a time-changed Brownian motion coupled to a Gamma Levy subordinator and…
In exponential semi-martingale setting for risky asset we estimate the difference of prices of options when initial physical measure $P$ and corresponding martingale measure $Q$ change to $\tilde{P}$ and $\tilde{Q}$ respectively. Then, we…
This paper studies an equity market of stochastic dimension, where the number of assets fluctuates over time. In such a market, we develop the fundamental theorem of asset pricing, which provides the equivalence of the following statements:…
Preferential Bayesian optimization allows optimization of objectives that are either expensive or difficult to measure directly, by relying on a minimal number of comparative evaluations done by a human expert. Generating candidate…
In this article we propose a novel approach to reduce the computational complexity of various approximation methods for pricing discrete time American options. Given a sequence of continuation values estimates corresponding to different…
We compare static arbitrage price bounds on basket calls, i.e. bounds that only involve buy-and-hold trading strategies, with the price range obtained within a multi-variate generalization of the Black-Scholes model. While there is no gap…
We argue for supplementing the process of training a prediction algorithm by setting up a scheme for detecting the moment when the distribution of the data changes and the algorithm needs to be retrained. Our proposed schemes are based on…
With reference to a single mediator context, this brief report presents a model-based strategy to estimate counterfactual direct and indirect effects when the response variable is ordinal and the mediator is binary. Postulating a logistic…
We consider a general class of continuous asset price models where the drift and the volatility functions, as well as the driving Brownian motions, change at a random time $\tau$. Under minimal assumptions on the random time and on the…
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…
We develop a numerical method for the martingale analogue of the Benamou--Brenier optimal transport problem, which seeks a martingale interpolating two prescribed marginals which is closest to the Brownian motion. Recent contributions have…
This paper deals with a high-order accurate implicit finite-difference approach to the pricing of barrier options. In this way various types of barrier options are priced, including barrier options paying rebates, and options on…
This paper proposes a novel model of financial prices where: (i) prices are discrete; (ii) prices change in continuous time; (iii) a high proportion of price changes are reversed in a fraction of a second. Our model is analytically…
We consider a trader who aims to liquidate a large position in the presence of an arbitrageur who hopes to profit from the trader's activity. The arbitrageur is uncertain about the trader's position and learns from observed price…
Consider a market of competing model providers selling query access to models with varying costs and capabilities. Customers submit problem instances and are willing to pay up to a budget for a verifiable solution. An arbitrageur…
This paper proposed a methodology to forecast electoral outcomes using the result of the combination of a fundamental model and a model-based aggregation of polls. We propose a Bayesian hierarchical structure for the fundamental model that…
In this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite…
We present an approach, based on deep neural networks, that allows identifying robust statistical arbitrage strategies in financial markets. Robust statistical arbitrage strategies refer to trading strategies that enable profitable trading…
New proofs are given of the existence of the compensator (or dual predictable projection) of a locally integrable c\'adl\'ag adapted process of finite variation and of the existence of the quadratic variation process for a c\'adl\'ag local…