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We consider the problem of supply and demand balancing that is stated as a minimization problem for the total expected revenue function describing the behavior of both consumers and suppliers. In the considered market model we assume that…
We pursue the quantum-mechanical challenge to the efficient market hypothesis for the stock market by employing the quantum Brownian motion model. We utilize the quantum Caldeira-Leggett master equation as a possible phenomenological model…
Due to the increasing popularity of futures trading among financial market participants, the risk management of these instruments is crucial. In this paper, we introduce a model for estimating the ideal time for leaving a trading position…
This paper discusses the connection between mathematical finance and statistical modelling which turns out to be more than a formal mathematical correspondence. We like to figure out how common results and notions in statistics and their…
In this paper we study the short-time behavior of the at-the-money implied volatility for European and arithmetic Asian call options with fixed strike price. The asset price is assumed to follow the Bachelier model with a general stochastic…
We consider a dynamic portfolio optimization problem that incorporates predictable returns, instantaneous transaction costs, price impact, and stochastic volatility, extending the classical results of Garleanu and Pedersen (2013), which…
We analyze the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the diffusion coefficients may grow faster than linearly and degenerate on the boundaries of…
We proposed a model of interacting market agents based on the Ising spin model. The agents can take three actions: "buy," "sell," or "stay inactive." We defined a price evolution in terms of the system magnetization. The model reproduces…
We consider stochastic volatility models under parameter uncertainty and investigate how model derived prices of European options are affected. We let the pricing parameters evolve dynamically in time within a specified region, and…
We introduce the stochastic multiplicative point process modelling trading activity of financial markets. Such a model system exhibits power-law spectral density S(f) ~ 1/f**beta, scaled as power of frequency for various values of beta…
We investigate the problem of pricing derivatives under a fractional stochastic volatility model. We obtain an approximate expression of the derivative price where the stochastic volatility can be composed of deterministic functions of time…
Some expansion methods have been proposed for approximately pricing options which has no exact closed formula. Benhamou et al. (2010) presents the smart expansion method that directly expands the expectation value of payoff function with…
A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique…
We present an analytical method to estimate the continuous-time collision probability of motion plans for autonomous agents with linear controlled Ito dynamics. Motion plans generated by planning algorithms cannot be perfectly executed by…
A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov…
The theta process is a stochastic process of number theoretical origin arising as a scaling limit of quadratic Weyl sums. It can be described in terms of the geodesic flow and an automorphic function on a homogeneous space. This process has…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
We propose and discuss some toy models of stock markets using the same operatorial approach adopted in quantum mechanics. Our models are suggested by the discrete nature of the number of shares and of the cash which are exchanged in a real…
In this paper, we propose the uncertain volatility models with stochastic bounds. Like the regular uncertain volatility models, we know only that the true model lies in a family of progressively measurable and bounded processes, but instead…
This paper uses new and recently established methodologies to study the evolutionary dynamics of the cryptocurrency market, and compares the findings with that of the equity market. We begin by applying random matrix theory and principal…