The model derives risky corporate bond prices (or equivalently credit spreads) subject to credit default and migration risk, based on an extended version of the Jarrow, Lando and Turnbull model, under a risk-neutral framework, as a result of the simulation of a continuous time, time-homogeneous...

Methods for leader's detection and overthrow in networks are useful tools for decision-making in many real-life cases, such as criminal networks with hidden patterns or money laundering networks. In the given research, we represent the algorithms that detect and overthrow the most influential...

SABR stochastic volatility model is appealing for modeling smile and skew of option prices. Hagan, who first proposed this model, derived a closed form approximation for european options and showed that it provides consistent and stable hedges. Here I prove a new exact closed formula for the...

A State's GDP represents the aggregated image of economic outcomes. Both the GDP dimension and its structure constitute important information with respect to the degree of economic development of a State. A State's GDP is a system characterised by increased inertia. For this reason, transition...

We give a functional description of the space of stochastic integrals with respect to a given family of martingales, based on the notion of direct integral of Hilbert spaces. We define the multiplicity function of a filtration and show, using our Hilbert space construction, that the multiplicity...

We develop a concept of a quot;domineering claimquot; and apply it to the existence, uniqueness and properties of optimal stopping times in continuous time. The notion pinpoints a key observation of pathwise optimality in Davis and Karatzas [8]. It also ties in well with several formulations of...

Modern portfolio theory produces optimal portfolios from estimates of expected returns and a covariance matrix. Such optimal portfolios are efficient portfolios, that is they provide the maximum level of expected return for a given level of risk. We present a method for portfolio selection based...

General deviation measures are introduced and studied systematically for their potential applications to risk management in areas like portfolio optimization and engineering. Such measures include standard deviation as a special case but need not be symmetric with respect to ups and downs. Their...

A new relationship is derived for net present value (NPV) per dollar invested that is composed entirely of interest rates. The rates are mark-ups to the cost of capital, each mark-up being an internal rate of return (IRR) embedded in the complex plane. The result has been shown before, but only...

In this paper we develop a class of applied probabilistic continuous time but discretized state space decompositions of the characterization of a multivariate generalized diffusion process. This decomposition is novel and, in particular, it allows one to construct families of mimicking classes...