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We consider the problem of a firm seeking to use personalized pricing to sell an exogenously given stock of a product over a finite selling horizon to different consumer types. We assume that the type of an arriving consumer can be observed…
We propose the deep parametric PDE method to solve high-dimensional parametric partial differential equations. A single neural network approximates the solution of a whole family of PDEs after being trained without the need of sample…
We consider an optimal investment problem to maximize expected utility of the terminal wealth, in an illiquid market with search frictions and transaction costs. In the market model, an investor's attempt of transaction is successful only…
We study the explicit calculation of the set of superhedging portfolios of contingent claims in a discrete-time market model for d assets with proportional transaction costs. The set of superhedging portfolios can be obtained by a recursive…
A classical inventory problem is studied from the perspective of embedded options, reducing inventory-management to the design of optimal contracts for forward delivery of stock (commodity). Financial option techniques \`{a} la…
The BS equations with fractional order two asset price models give a better prediction of options pricing in the monetary market. In this paper, the changed form of BS-condition with two asset price models dependent on the Liovelle-Caputo…
In a market with one safe and one risky asset, an investor with a long horizon, constant investment opportunities, and constant relative risk aversion trades with small proportional transaction costs. We derive explicit formulas for the…
The derivative expansion of the effective action is considered in the model with two interacting real scalar fields in curved spacetime. Using the functional approach and local momentum representation, the coefficient of the derivative term…
We consider the multi-refraction strategies in two equivalent versions of the optimal dividend problem in the dual (spectrally positive L\'evy) model. The first problem is a variant of the bail-out case where both dividend payments and…
We study the optimal solution to a general two-slope ski rental problem with a tail risk, i.e., the chance of the competitive ratio exceeding a value $\gamma$ is bounded by $\delta$. This extends the recent study of tail bounds for ski…
We consider a stochastic financial incomplete market where the price processes are described by a vector-valued semimartingale that is possibly nonlocally bounded. We face the classical problem of utility maximization from terminal wealth,…
The theory of optimal trading under proportional transaction costs has been considered from a variety of perspectives. In this paper, we show that all the results can be interpreted using a universal law, illustrating the results in trading…
This paper studies the continuous-time pre-commitment KMM problem proposed by Klibanoff, Marinacci and Mukerji (2005) in incomplete financial markets, which concerns with the portfolio selection under smooth ambiguity. The decision maker…
We develop a new class of path transformations for one-dimensional diffusions that are tailored to alter their long-run behaviour from transient to recurrent or vice versa. This immediately leads to a formula for the distribution of the…
In this paper is investigated the pricing problem of options on bonds with credit risk based on analysis on two kinds of solving problems for the Black-Scholes equations. First, a solution representation of the Black-Scholes equation with…
We adopt deep learning models to directly optimise the portfolio Sharpe ratio. The framework we present circumvents the requirements for forecasting expected returns and allows us to directly optimise portfolio weights by updating model…
The Black-Scholes option pricing model remains a cornerstone in financial mathematics, yet its application is often challenged by the need for accurate hedging strategies, especially in dynamic market environments. This paper presents a…
This paper explores the use of the multinode Shepard method for the numerical solution of the two-dimensional Black-Scholes equation. The proposed approach integrates a spatial approximation via the multinode Shepard operator with a…
We consider an investor who is dynamically informed about the future evolution of one of the independent Brownian motions driving a stock's price fluctuations. With linear temporary price impact the resulting optimal investment problem with…
We assume a continuous-time price impact model similar to Almgren-Chriss but with the added assumption that the price impact parameters are stochastic processes modeled as correlated scalar Markov diffusions. In this setting, we develop…