arXiv · arXiv q-fin · 2025
Turnpike theorems state that if an investor's utility is asymptotically equivalent to a power utility, then the optimal investment strategy converges to the CRRA strategy as the investment horizon tends to infinity. This paper aims to derive the convergence rates of the turnpike theorem for optimal feedback functions in stochastic factor models. In these models, optimal feedback functions can be decomposed into two t…
Hiroki Yamamichi
arXiv · arXiv · 2016
In this survey paper we discuss recent advances on short interest rate models which can be formulated in terms of a stochastic differential equation for the instantaneous interest rate (also called short rate) or a system of such equations in case the short rate is assumed to depend also on other stochastic factors. Our focus is on convergence models, which explain the evolution of interest rate in connection with th…
Zuzana Buckova, Beata Stehlikova, Daniel Sevcovic
arXiv · arXiv · 2025
We propose a structural default model for portfolio-wide valuation adjustments (xVAs) and represent it as a system of coupled backward stochastic differential equations. The framework is divided into four layers, each capturing a key component: (i) clean values, (ii) initial margin and Collateral Valuation Adjustment (ColVA), (iii) Credit/Debit Valuation Adjustments (CVA/DVA) together with Margin Valuation Adjustment…
Kristoffer Andersson, Alessandro Gnoatto
arXiv · arXiv · 2023
In the setting of stochastic Volterra equations, and in particular rough volatility models, we show that conditional expectations are the unique classical solutions to path-dependent PDEs. The latter arise from the functional Itô formula developed by [Viens, F., & Zhang, J. (2019). A martingale approach for fractional Brownian motions and related path dependent PDEs. Ann. Appl. Probab.]. We then leverage these tools …
Ofelia Bonesini, Antoine Jacquier, Alexandre Pannier
arXiv · arXiv · 2022
Nonlinear Markov Chains (nMC) are regarded as the original (linear) Markov Chains with nonlinear small perturbations. It fits real-world data better, but its associated properties are difficult to describe. A new approach is proposed to analyze the ergodicity and even estimate the convergence bounds of nMC, which is more precise than existing results. In the new method, Coupling Markov about homogeneous Markov chains…
Kaichen Xu
arXiv · arXiv · 2021
We study the convergence properties of the short maturity expansion of option prices in the uncorrelated log-normal ($β=1$) SABR model. In this model the option time-value can be represented as an integral of the form $V(T) = \int_{0}^\infty e^{-\frac{u^2}{2T}} g(u) du$ with $g(u)$ a "payoff function" which is given by an integral over the McKean kernel $G(s,t)$. We study the analyticity properties of the function $g…
Alan L. Lewis, Dan Pirjol
arXiv · arXiv · 2019
We analyze the probability of ruin for the {\it scaled} classical Cramér-Lundberg (CL) risk process and the corresponding diffusion approximation. The scaling, introduced by Iglehart \cite{I1969} to the actuarial literature, amounts to multiplying the Poisson rate $\la$ by $n$, dividing the claim severity by $\sqrtn$, and adjusting the premium rate so that net premium income remains constant. %Therefore, we think of …
Asaf Cohen, Virginia R. Young
arXiv · arXiv · 2015
This paper studies convergence properties of multivariate distributions constructed by endowing empirical margins with a copula. This setting includes Latin Hypercube Sampling with dependence, also known as the Iman--Conover method. The primary question addressed here is the convergence of the component sum, which is relevant to risk aggregation in insurance and finance. This paper shows that a CLT for the aggregated…
Georg Mainik
arXiv · arXiv · 2015
We study the Heston-Cox-Ingersoll-Ross++ stochastic-local volatility model in the context of foreign exchange markets and propose a Monte Carlo simulation scheme which combines the full truncation Euler scheme for the stochastic volatility component and the stochastic domestic and foreign short interest rates with the log-Euler scheme for the exchange rate. We establish the exponential integrability of full truncatio…
Andrei Cozma, Matthieu Mariapragassam, Christoph Reisinger
arXiv · arXiv · 2013
Cubature on Wiener space [Lyons, T.; Victoir, N.; Proc. R. Soc. Lond. A 8 January 2004 vol. 460 no. 2041 169-198] provides a powerful alternative to Monte Carlo simulation for the integration of certain functionals on Wiener space. More specifically, and in the language of mathematical finance, cubature allows for fast computation of European option prices in generic diffusion models. We give a random walk interpreta…
Christian Bayer, Peter K. Friz
arXiv · arXiv · 2013
In this article we study the convergence of a European lookback option with floating strike evaluated with the binomial model of Cox-Ross-Rubinstein to its evaluation with the Black-Scholes model. We do the same for its delta. We confirm that these convergences are of order 1/Sqrt(n). For this, we use the binomial model of Cheuk-Vorst which allows us to write the price of the option using a double sum. Based on an im…
Fabien Heuwelyckx
arXiv · arXiv q-fin · 2026
We consider an optimal trading problem under a market impact model with endogenous market resistance generated by a sophisticated trader who (partially) detects metaorders and trades against them to exploit price overreactions induced by the order flow. The model features a concave transient impact driven by a power-law propagator with a resistance term responding to the trader's rate via a fixed-point equation invol…
Nathan De Carvalho, Youssef Ouazzani Chahdi, Grégoire Szymanski
arXiv · arXiv q-fin · 2026
April 2026 saw notable methodological convergence in the academic study of informed trading on decentralized prediction markets. Three approaches surfaced almost simultaneously: Mitts and Ofir (2026) apply a composite screen to over 210,000 wallet-market pairs; Gomez-Cram et al. (2026) apply an event-level sign-randomization test to Polymarket's complete transaction history, classifying 3.14% of accounts as "skilled …
Maksym Nechepurenko
arXiv · arXiv · 2026
We study the quadratic tracking problem of a general stochastic target process with absolutely continuous controls, with and without terminal constraint. We derive explicit, non-asymptotic upper bounds in terms of a Besov-type modulus of the target. These bounds yield sharp explicit rates that specialize to the square-root order for semimartingale targets. We then apply these results to a generalized Obizhaeva--Wang …
Marcel Nutz, Moritz Voss
arXiv · arXiv q-fin · 2025
Considering the continuous-time Mean-Variance (MV) portfolio optimization problem, we study a regime-switching market setting and apply reinforcement learning (RL) techniques to assist informed exploration within the control space. We introduce and solve the Exploratory Mean Variance with Regime Switching (EMVRS) problem. We also present a Policy Improvement Theorem. Further, we recognize that the widely applied Temp…
Yuling Max Chen, Bin Li, David Saunders
arXiv · arXiv q-fin · 2024
In this paper, we present an artificial neural network framework for portfolio compression of a large portfolio of European options with varying maturities (target portfolio) by a significantly smaller portfolio of European options with shorter or same maturity (compressed portfolio), which also represents a self-replicating static hedge portfolio of the target portfolio. For the proposed machine learning architectur…
Vikranth Lokeshwar Dhandapani, Shashi Jain
arXiv · arXiv q-fin · 2020
In quantitative finance, modeling the volatility structure of underlying assets is vital to pricing options. Rough stochastic volatility models, such as the rough Bergomi model [Bayer, Friz, Gatheral, Quantitative Finance 16(6), 887-904, 2016], seek to fit observed market data based on the observation that the log-realized variance behaves like a fractional Brownian motion with small Hurst parameter, $H < 1/2$, over …
Christian Bayer, Eric Joseph Hall, Raúl Tempone
arXiv · arXiv · 2026
Foster and Viswanathan (1996) extend the discrete-time setting of Kyle (1985) to multiple informed traders who have partial information about the stock's terminal dividend. We resolve two long-standing open problems in this literature. First, we prove that an equilibrium exists in the setting of Foster and Viswanathan (1996). Second, as the number of trading times goes to infinity, we prove that the discrete-time equ…
Jin Choi, Kasper Larsen