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.
This paper extends Markovian projections to semimartingales with jumps.
Study robust utility maximization with uncertain continuous semimartingales.
We derive asymptotic expansions for option data to detect infinite variation volatility.
Paper investigates existence of deflators in financial markets.
In this paper we study time-inhomogeneous affine processes beyond the common assumption of stochastic continuity. In this setting times of jumps can be both inaccessible and predictable. To this end we develop a general theory of finite dimensional affine semimartingales under very weak assumptions. We show that the co…
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…
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…
The paper simplifies calculus for semimartingales using multiplicative compensation.
We derive a higher-order expansion for rough volatility models.
The paper revisits expected signatures in semimartingale models, providing new formulae and simplifying complexity.
In this paper, we study the ruin problem with investment in a general framework where the business part X is a L{é}vy process and the return on investment R is a semimartingale. We obtain upper bounds on the finite and infinite time ruin probabilities that decrease as a power function when the initial capital increases…
Constructs rank-based continuous semimartingales for financial markets.
We study the existence of the numeraire portfolio under predictable convex constraints in a general semimartingale model of a financial market. The numeraire portfolio generates a wealth process, with respect to which the relative wealth processes of all other portfolios are supermartingales. Necessary and sufficient c…
In Karatzas and Kardaras's paper on semimartingale financial models, it is proved that the NUPBR condition is a property of the local characteristic of the asset process alone. In Takaoka's paper on NUPBR, it is proved that the NUPBR condition is equivalent to the existence of a simga-martingale deflator. However, Taka…
The paper studies horizontal semimartingales on Riemannian manifolds and their connections to Euclidean spaces.
Simplified calculus for semimartingales makes complex transformations easier.
Study forward investment performance in semimartingale markets with stochastic factors.
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…
No arbitrage in financial markets with special semimartingales.
We propose a unified analysis of a whole spectrum of no-arbitrage conditions for financial market models based on continuous semimartingales. In particular, we focus on no-arbitrage conditions weaker than the classical notions of No Arbitrage and No Free Lunch with Vanishing Risk. We provide a complete characterisation…
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…
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…
Unified framework for optimal liquidation with small market impact and semimartingale strategies.
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…
The Markowitz problem consists of finding in a financial market a self-financing trading strategy whose final wealth has maximal mean and minimal variance. We study this in continuous time in a general semimartingale model and under cone constraints: Trading strategies must take values in a (possibly random and time-de…
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 …
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…
Paper introduces second-order Esscher densities for continuous-time models.
New results on financial equilibria in markets with general semimartingales.
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).
Rough volatility models are very appealing because of their remarkable fit of both historical and implied volatilities. However, due to the non-Markovian and non-semimartingale nature of the volatility process, there is no simple way to simulate efficiently such models, which makes risk management of derivatives an int…
Kramkov and Sirbu (2006, 2007) have shown that first-order approximations of power utility-based prices and hedging strategies can be computed by solving a mean-variance hedging problem under a specific equivalent martingale measure and relative to a suitable numeraire. In order to avoid the introduction of an addition…
A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the discounted asset-price process - in particular, the semimartingale property is not assumed. Via a natural market viability assumption, namely, absence of arbitrages of t…
Extends credit risky bond market models to include jumps and general semimartingales.
Paper approximates rough stochastic local volatility models for efficient computation.
Suppose that are continuous semimartingales that are reversible and have nondegenerate crossings. Then the corresponding rank processes can be represented by generalized Stratonovich integrals, and this representation can be used to decompose the relative log-return of portfolios generated by functi…
The purpose of this paper is two-fold. First is to extend the notions of an n-dimensional semimartingale and its stochastic integral to a piecewise semimartingale of stochastic dimension. The properties of the former carry over largely intact to the latter, avoiding some of the pitfalls of infinite-dimensional stochast…
Researchers derive an analytic expression for Gaussian stochastic volatility models.
For utility functions finite valued on , we prove a duality formula for utility maximization with random endowment in general semimartingale incomplete markets. The main novelty of the paper is that possibly non locally bounded semimartingale price processes are allowed. Following Biagini and Frittelli …
We derive a forward partial integro-differential equation for prices of call options in a model where the dynamics of the underlying asset under the pricing measure is described by a -possibly discontinuous- semimartingale. A uniqueness theorem is given for the solutions of this equation. This result generalizes Dupire…
Given a finite honest time, we first show that the associated Azéma optional supermartingale can be expressed as the drawdown and the relative drawdown of some local optional supermartingales with continuous running supremum. The relative drawdown representation then allows us to provide a characterisation of finite ho…
Stochastic integrals are defined with respect to a collection of continuous semimartingales, imposing no assumptions on the index set and the subspace of where takes values. The integrals are constructed though finite-dimensional approximation, identifying the appropriate …
This thesis is devoted to the study of affine processes and their applications in financial mathematics. In the first part we consider the theory of time-inhomogeneous affine processes on general state spaces. We present a concise setup for time-inhomogeneous Markov processes. For stochastically continuous affine proce…
I prove that every adapted Brownian bridge on a geodesically complete connected Riemannian manifold is a semimartingale including its terminal time, without any further assumptions on the geometry. In particular, it follows that every such process can be horizontally lifted to a smooth principal fiber bundle with conne…
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…