相关论文: Ruin Probabilities for a Sparre Andersen Model wit…
It is shown that the celebrated result of Sparre Andersen for random walks and L\'evy processes has intriguing consequences when the last time of the process in $(-\infty,0]$, say $\sigma$, is added to the picture. In the case of no…
We give a new predictive mathematical model for macroeconomics, which deals specifically with asset prices and earnings fluctuations, in the presence of a dynamic economy involving mergers, acquisitions, and hostile takeovers. Consider a…
We introduce the concept of cumulative Parisian ruin, which is based on the time spent in the red by the underlying surplus process. Our main result is an explicit representation for the distribution of the occupation time, over a…
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…
The current research on credit risk is primarily focused on modeling default probabilities. Recovery rates are often treated as an afterthought; they are modeled independently, in many cases they are even assumed constant. This is despite…
We analyze operational risk in terms of a spin glass model. Several regimes are investigated, as a functions of the parameters that characterize the dynamics. The system is found to be robust against variations of these parameters. We…
In this paper, we describe two approaches to model the behavior of stock prices. The first approach considers the underlying probability distribution of day-to-day price differences. The second approach models the movement of the price as a…
We use standard physics techniques to model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties…
A simple spin system is constructed to simulate dynamics of asset prices and studied numerically. The outcome for the distribution of prices is shown to depend both on the dimension of the system and the introduction of price into the link…
Asset prices contain information about the probability distribution of future states and the stochastic discounting of those states as used by investors. To better understand the challenge in distinguishing investors' beliefs from…
We analyze the general L\'{e}vy insurance risk process for L\'{e}vy measures in the convolution equivalence class $\mathcal{S}^{(\alpha)}$, $\alpha>0$, via a new kind of path decomposition. This yields a very general functional limit…
We study the default risk in incomplete information. That means, we model the value of a firm by one L\'evy process which is the sum of brownian motion with drift and compound Poisson process. This L\'evy process can not be observed…
Standard models of asset price dynamics, such as geometric Brownian motion (see, for example, Osborne, 1959, Samuelson, 2016), do not formally incorporate investor inertia. This paper presents a two-stage framework for modelling this…
We develop a theoretical trading conditioning model subject to price volatility and return information in terms of market psychological behavior, based on analytical transaction volume-price probability wave distributions in which we use…
We analyze the problem of the analytical characterization of the probability distribution of financial returns in the exponential Ornstein-Uhlenbeck model with stochastic volatility. In this model the prices are driven by a Geometric…
This paper investigates asymptotic estimates for the entrance probability of the discounted aggregate claim vector from a multivariate renewal risk model into some rare set. We provide asymptotic results for the entrance probability on both…
Maximum likelihood estimation applied to high-frequency data allows us to quantify intermittency in the fluctu- ations of asset prices. From time records as short as one month these methods permit extraction of a meaningful intermittency…
We solve exactly a simple model of trend following strategy, and obtain the analytical shape of the profit per trade distribution. This distribution is non trivial and has an option like, asymmetric structure. The degree of asymmetry…
An asset pricing model using long-run capital share growth risk has recently been found to successfully explain U.S. stock returns. Our paper adopts a recursive preference utility framework to derive an heterogeneous asset pricing model…
The Cram\'er-Lundberg model with exponential claims and proportional investment is solved exactly: the integro-differential equation for the survival probability reduces to a doubly confluent Heun equation, yielding an explicit solution in…