相关论文: Continuous-time trading and emergence of volatilit…
Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the…
Perpetual American options are financial instruments that can be readily exercised and do not mature. In this paper we study in detail the problem of pricing this kind of derivatives, for the most popular flavour, within a framework in…
We introduce, in continuous time, an axiomatic approach to assign to any financial position a dynamic ask (resp. bid) price process. Taking into account both transaction costs and liquidity risk this leads to the convexity (resp. concavity)…
We consider a process $X_t$, which is observed on a finite time interval $[0,T]$, at discrete times $0,\Delta_n,2\Delta_n,\ldots.$ This process is an It\^{o} semimartingale with stochastic volatility $\sigma_t^2$. Assuming that $X$ has…
Identifying behavior that is relatively invariant under different conditions is a challenging task in far-from-equilibrium complex systems. As an example of how the existence of a semi-invariant signature can be masked by the heterogeneity…
The aim of this work consists in the study of the optimal investment strategy for a behavioural investor, whose preference towards risk is described by both a probability distortion and an S-shaped utility function. Within a continuous-time…
The stability of money value is an important requisite for a functioning economy, yet it critically depends on the actions of participants in the market themselves. Here we model the value of money as a dynamical variable that results from…
The relationship between price volatilty and a market extremum is examined using a fundamental economics model of supply and demand. By examining randomness through a microeconomic setting, we obtain the implications of randomness in the…
In this paper we present a continuous time dynamical model of heterogeneous agents interacting in a financial market where transactions are cleared by a market maker. The market is composed of fundamentalist, trend following and contrarian…
Without probability theory, we define classes of supermartingales, martingales, and semimartingales in idealized financial markets with continuous price paths. This allows us to establish probability-free versions of a number of standard…
Existence of stochastic financial equilibria giving rise to semimartingale asset prices is established under a general class of assumptions. These equilibria are expressed in real terms and span complete markets or markets with withdrawal…
We introduce a new class of continuous-time models of the stochastic volatility of asset prices. The models can simultaneously incorporate roughness and slowly decaying autocorrelations, including proper long memory, which are two stylized…
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…
A pricing principle is introduced for non-attainable $q$-exponential bounded contingent claims in an incomplete Brownian motion market setting. The buyer evaluates the contingent claim under the ``distorted Radon-Nikodym derivative'' and…
The general method is proposed for constructing a family of martingale measures for a wide class of evolution of risky assets. The sufficient conditions are formulated for the evolution of risky assets under which the family of equivalent…
It is well-known that well-posedness of a martingale problem in the class of continuous (or r.c.l.l.) solutions enables one to construct the associated transition probability functions. We extend this result to the case when the martingale…
In this paper we extend discrete time semi-static trading strategies by also allowing for dynamic trading in a finite amount of options, and we study the consequences for the model-independent super-replication prices of exotic derivatives.…
The observation of power laws in the time to extrema of volatility, volume and intertrade times, from milliseconds to years, are shown to result straightforwardly from the selection of biased statistical subsets of realizations in otherwise…
In this article, we show necessary and sufficient conditions for a function to transform a continuous Markov semimartingale to a semimartingale. As a result, the no-arbitrage principle guarantees the differentiability of asset prices with…
We document and analyze the empirical facts concerning one of the clearest evidence of speculation in financial trading as observed in the postage collection stamp market. We unravel some of the mechanisms of speculative behavior which…