arXiv research

Study approximates financial market with discrete-time models.

Study of discrete-time mean-variance model using reinforcement learning.

Consider power utility maximization of terminal wealth in a 1-dimensional continuous-time exponential Levy model with finite time horizon. We discretize the model by restricting portfolio adjustments to an equidistant discrete time grid. Under minimal assumptions we prove convergence of the optimal discrete-time strate…

Defines speculative bubbles in discrete-time models based on discounted stock price losing mass.

Study proves existence and convergence of discrete-time Kyle models with multiple insiders.

This paper studies the properties of discrete time stochastic optimal control problems associated with portfolio selection. We investigate if optimal continuous time strategies can be used effectively for a discrete time market after a straightforward discretization. We found that Merton's strategy approximates the per…

RL solves discrete LQ control with Gaussian optimal policy.

Characterizes super-replication prices in a financial market model.

Safety filter for unknown discrete-time systems with learned models and noise covariance.

We study asymptotic properties of some (essentially conditional least squares) parameter estimators for the subcritical Heston model based on discrete time observations derived from conditional least squares estimators of some modified parameters.

Study optimal hedging for claims with random weights in discrete time.

We consider a discrete-time financial market model with finite time horizon and give conditions which guarantee the existence of an optimal strategy for the problem of maximizing expected terminal utility. Equivalent martingale measures are constructed using optimal strategies.

Paper develops a continuous-time framework for financial markets without stochastic calculus.

We investigate the possibility of statistical evaluation of the market completeness for discrete time stock market models. It is known that the market completeness is not a robust property: small random deviations of the coefficients convert a complete market model into a incomplete one. The paper shows that market inc…

Study asset pricing under model uncertainty with discrete time and states.

Optimal strategy for liquidating portfolios under discrete time intervals.

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 expected shortfall under a cost constraint and show that these problems can be trea…

We unify and establish equivalence between the pathwise and the quasi-sure approaches to robust modelling of financial markets in discrete time. In particular, we prove a Fundamental Theorem of Asset Pricing and a Superhedging Theorem, which encompass the formulations of [Bouchard, B., & Nutz, M. (2015). Arbitrage and …

We give a general formulation of the utility maximization problem under nondominated model uncertainty in discrete time and show that an optimal portfolio exists for any utility function that is bounded from above. In the unbounded case, integrability conditions are needed as nonexistence may arise even if the value fu…

Semistatic trading strategies can be taken to limits in discrete time.

Continuous time models in the theory of real options give explicit formulas for optimal exercise strategies when options are simple and the price of an underlying asset follows a geometric Brownian motion. This paper suggests a general, computationally simple approach to real options in discrete time. Explicit formulas…

We obtain a constructive criterion for robust no-arbitrage in discrete-time market models with transaction costs. This criterion is expressed in terms of the supports of the regular conditional upper distributions of the solvency cones. We also consider the model with a bank account. A method for construction of arbitr…

This paper derives a diffusion approximation for a sequence of discrete-time one-sided limit order book models with non-linear state dependent order arrival and cancellation dynamics. The discrete time sequences are specified in terms of an $\R_+$-valued best bid price process and an $L^2_{loc}$-valued volume process. …

This paper investigates the problem of maximizing expected terminal utility in a discrete-time financial market model with a finite horizon under non-dominated model uncertainty. We use a dynamic programming framework together with measurable selection arguments to prove that under mild integrability conditions, an opt…

Study arbitrage in financial markets with trading restrictions.

The paper studies market viability and completeness in discrete markets.

Study bounds for European basket call options in a discrete-time market model with price jumps.

Paper introduces dynamic strategies for multi-period investment models.

We prove existence of a self-financing strategy which minimizes shortfall for game options in discrete time

We find a normal form for two-input flat discrete-time systems.

PyDTS analyzes survival data with discrete intervals and competing risks.

Discrete-time systems can be characterized by simple flat coordinates and their shifts.

The time average of geometric Brownian motion plays a crucial role in the pricing of Asian options in mathematical finance. In this paper we consider the asymptotics of the discrete-time average of a geometric Brownian motion sampled on uniformly spaced times in the limit of a very large number of averaging time steps.…

The paper analyzes the probabilistic structure of DDPMs and bounds their sampling error.

We introduce a setup of model uncertainty in discrete time. In this setup we derive dual expressions for the super--replication prices of game options with upper semicontinuous payoffs. We show that the super--replication price is equal to the supremum over a special (non dominated) set of martingale measures, of the c…

Building on the work of Schweizer (1995) and Cern and Kallseny (2007), we present discrete time formulas minimizing the mean square hedging error for multidimensional assets. In particular, we give explicit formulas when a regime-switching random walk or a GARCH-type process is utilized to model the returns. Monte Carl…

We develop theory and applications of forward characteristic processes in discrete time following a seminal paper of Jan Kallsen and Paul Krühner. Particular emphasis is placed on the dynamics of volatility surfaces which can be easily formulated and implemented from the chosen discrete point of view. In mathematical t…

We study the superreplication of contingent claims under model uncertainty in discrete time. We show that optimal superreplicating strategies exist in a general measure-theoretic setting; moreover, we characterize the minimal superreplication price as the supremum over all continuous linear pricing functionals on a sui…

This note develops an arbitrage theory for a discrete-time market model without the assumption of the existence of a numéraire asset. Fundamental theorems of asset pricing are stated and proven in this context. The distinction between the notions of investment-consumption arbitrage and pure-investment arbitrage provide…

Study shows financial value of weak information converges in discrete vs continuous markets.

We study a robust stochastic optimization problem in the quasi-sure setting in discrete-time. We show that under a lineality-type condition the problem admits a maximizer. This condition is implied by the no-arbitrage condition in models of financial markets. As a corollary, we obtain existence of an utility maximizer …

Optimizes control of noisy discrete systems without system matrix knowledge.

Solves super-hedging for financial models with uncertain prices.

Kyle's equilibrium model stability proven for 1-2 trading times, but not for 3 or more.

This paper deals with the problem of discrete-time option pricing by the mixed fractional version of Merton model with transaction costs. By a mean-self-financing delta hedging argument in a discrete-time setting, a European call option pricing formula is obtained. We also investigate the effect of the time-step $δt$ a…

The paper proves that linearization along trajectories preserves flatness in discrete-time systems.

Paper formulates mutual information optimal control for discrete-time systems.

Neural nets replicate hedging payoffs for realistic discrete-time settings.