A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Method calibrates local volatility and stochastic short rate models for equity-rate dynamics.
The paper calibrates SPX and VIX options using optimal transport.
In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent constraints. Duality results are established, representing the solution in terms of path d…
Method calibrates stock price models with stochastic interest rates using optimal transport.
Unified framework for optimal liquidation with small market impact and semimartingale strategies.
In quantitative finance, we often fit a parametric semimartingale model to asset prices. To ensure our model is correct, we must then perform goodness-of-fit tests. In this paper, we give a new goodness-of-fit test for volatility-like processes, which is easily applied to a variety of semimartingale models. In each cas…
Study robust utility maximization with uncertain continuous semimartingales.
A wealth-process set is abstractly defined to consist of nonnegative càdlàg processes containing a strictly positive semimartingale and satisfying an intuitive re-balancing property. Under the condition of absence of arbitrage of the first kind, it is established that all wealth processes are semimartingales and that t…
While absence of arbitrage in frictionless financial markets requires price processes to be semimartingales, non-semimartingales can be used to model prices in an arbitrage-free way, if proportional transaction costs are taken into account. In this paper, we show, for a class of price processes which are not necessaril…
Optimal trading strategies in fluctuating financial markets are analyzed using complex mathematical models.
We study utility maximization for power utility random fields with and without intermediate consumption in a general semimartingale model with closed portfolio constraints. We show that any optimal strategy leads to a solution of the corresponding Bellman equation. The optimal strategies are described pointwise in term…
We price and hedge American options robustly in continuous time.
Study optimizes portfolio liquidation strategies with complex market impacts.
In quantitative finance, we often model asset prices as semimartingales, with drift, diffusion and jump components. The jump activity index measures the strength of the jumps at high frequencies, and is of interest both in model selection and fitting, and in volatility estimation. In this paper, we give a novel estimat…
Study optimal liquidation strategies with infinite horizon and regime switching.
The paper studies horizontal semimartingales on Riemannian manifolds and their connections to Euclidean spaces.
Simplified calculus for semimartingales makes complex transformations easier.
Paper investigates existence of deflators in financial markets.
This paper extends Markovian projections to semimartingales with jumps.
Study forward investment performance in semimartingale markets with stochastic factors.
Projects Markovian processes from Itô semimartingales with jumps.
We study the short-time asymptotics of conditional expectations of smooth and non-smooth functions of a (discontinuous) Ito semimartingale; we compute the leading term in the asymptotics in terms of the local characteristics of the semimartingale. We derive in particular the asymptotic behavior of call options with sho…
New theorem handles stochastic Volterra semimartingales.
In a general semimartingale financial model, we study the stability of the No Arbitrage of the First Kind (NA1) (or, equivalently, No Unbounded Profit with Bounded Risk) condition under initial and under progressive filtration enlargements. In both cases, we provide a simple and general condition which is sufficient to…
We give a collection of explicit sufficient conditions for the true martingale property of a wide class of exponentials of semimartingales. We express the conditions in terms of semimartingale characteristics. This turns out to be very convenient in financial modeling in general. Especially it allows us to carefully di…
The paper simplifies calculus for semimartingales using multiplicative compensation.
No arbitrage in financial markets with special semimartingales.
We study dynamic optimal portfolio allocation for monotone mean--variance preferences in a general semimartingale model. Armed with new results in this area we revisit the work of Cui, Li, Wang and Zhu (2012, MAFI) and fully characterize the circumstances under which one can set aside a non-negative cash flow while sim…
This article studies the sensitivity of the power utility maximization problem with respect to the investor's relative risk aversion, the statistical probability measure, the investment constraints and the market price of risk. We extend previous descriptions of the dual domain then exploit the link between the constra…
In a recent work \cite{BG}, given a collection of continuous semimartingales, authors derive a semimartingale decomposition from the corresponding ranked processes in the case that the ranked processes can meet more than two original processes at the same time. This has led to a more general decomposition of ranked pro…
New approach avoids restrictive assumptions for optimal portfolio in default risk scenarios.
In this paper we study the asymptotic decay of finite time ruin probabilities for an insurance company that faces heavy-tailed claims, uses predictable investment strategies and makes investments in risky assets whose prices evolve according to quite general semimartingales. We show that the ruin problem corresponds to…
New methods estimate transport-growth pairs in unbalanced optimal transport.
Assuming geometric Brownian motion as unaffected price process , Gatheral & Schied (2011) derived a strategy for optimal order execution that reacts in a sensible manner on market changes but can still be computed in closed form. Here we will investigate the robustness of this strategy with respect to misspecifica…
Introduces statistical optimal transport for probabilistic lectures.
Paper solves Merton's portfolio problem in a non-Markovian, non-semimartingale model.
NOT learns optimal transport plans, kernel costs improve performance.
New algorithm solves unbalanced optimal transport on trees in quasi-linear time.
Existence of stochastic financial equilibria giving rise to semimartingale asset prices is established under a general class of assumptions. These equilibria are expressed in real terms and span complete markets or markets with withdrawal constraints.We deal with random endowment density streams which admit jumps and g…
In this work, we develop a novel principal component analysis (PCA) for semimartingales by introducing a suitable spectral analysis for the quadratic variation operator. Motivated by high-dimensional complex systems typically found in interest rate markets, we investigate correlation in high-dimensional high-frequency …
New results on financial equilibria in markets with general semimartingales.
Extends optimal transport to dynamic and martingale settings.
Paper relaxes optimal transport using convex functions for data science.
In this paper, we present a novel and principled approach to learn the optimal transport between two distributions, from samples. Guided by the optimal transport theory, we learn the optimal Kantorovich potential which induces the optimal transport map. This involves learning two convex functions, by solving a novel mi…
We present an elementary treatment of the Optional Decomposition Theorem for continuous semimartingales and general filtrations. This treatment does not assume the existence of equivalent local martingale measure(s), only that of strictly positive local martingale deflator(s).
New optimal transport method handles mass creation and destruction.
Review of modern computational optimal transport methods for biomedical applications.
Paper investigates optimal transport map estimation in infinite-dimensional spaces.