Related papers: On the average rate of return in a continuous time…
We present analytical investigations of a multiplicative stochastic process that models a simple investor dynamics in a random environment. The dynamics of the investor's budget, $x(t)$, depends on the stochasticity of the return on…
A growing empirical literature suggests that equity-premium predictability is state dependent, with much of the forecasting power concentrated around recessionary periods (Henkel et al., 2011; Dangl and Halling, 2012; Devpura et al., 2018).…
In the context of time-subordinated Brownian motion models, Fourier theory and methodology are proposed to modelling the stochastic distribution of time increments. Gaussian Variance-Mean mixtures and time-subordinated models are reviewed…
In markets with transaction costs, consistent price systems play the same role as martingale measures in frictionless markets. We prove that if a continuous price process has conditional full support, then it admits consistent price systems…
We consider the consumption-based asset pricing model, derive a new modified basic pricing equation, and present its successive approximations using the Taylor series expansions of the investor's utility during the averaging time interval.…
We prove the existence of a Radner equilibrium in a model with proportional transaction costs on an infinite time horizon and analyze the effect of transaction costs on the endogenously determined interest rate. Two agents receive…
We consider a tick-by-tick model of price formation, in which buy and sell orders are modeled as self-exciting point processes (Hawkes process), similar to the one in [Bacry, Delattre, Hoffmann, Muzy, Modelling microstructure noise with…
Price range contains important information about the asset volatility, and has long been considered an important indicator for it. In this paper, we propose to jointly model the [low, high] price range as a random interval and introduce an…
We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on linear self…
In this study, we introduce new estimation methods for the required rate of return of the stochastic dividend discount model (DDM) and the private company valuation model, which will appear below. To estimate the required rate of return, we…
"Fundamental theorem of asset pricing" roughly states that absence of arbitrage opportunity in a market is equivalent to the existence of a risk-neutral probability. We give a simple counterexample to this oversimplified statement. Prices…
This paper studies an asset pricing model in a partially observable market with a large number of heterogeneous agents using the mean field game theory. In this model, we assume that investors can only observe stock prices and must infer…
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…
A simple quantum model explains the Levy-unstable distributions for individual stock returns observed by ref.[1]. The probability density function of the returns is written as the squared modulus of an amplitude. For short time intervals…
Recent empirical studies suggest that the volatilities associated with financial time series exhibit short-range correlations. This entails that the volatility process is very rough and its autocorrelation exhibits sharp decay at the…
A novel version of the Continuous-Time Random Walk (CTRW) model with memory is developed. This memory means the dependence between arbitrary number of successive jumps of the process, while waiting times between jumps are considered as…
Stochastic network calculus is a newly developed theory for stochastic service guarantee analysis of computer networks. In the current stochastic network calculus literature, its fundamental models are based on the cumulative amount of…
What return should you expect when you take on a given amount of risk? How should that return depend upon other people's behavior? What principles can you use to answer these questions? In this paper, we approach these topics by exploring…
Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior…
A succesful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well chosen mean differential equation. Under an attainability condition,…