# Tagged Questions

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122 views

### Trouble verifying roll rate model

I found this paper on roll rate analysis via a google search. I would post a link, but every page is stamped with "CONFIDENTIAL" at the bottom (humorous since it is easily found). In a nut-shell, ...
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### pdf of simple equation, compound Poisson noise

I would like to find the probability density function (at stationarity) of the random variable $X_t$, where: \begin{equation*} dX_t = -aX_t dt + d N_t, \end{equation*} $a$ is a constant and $N_t$ is a ...
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### Prove that $E[g(X_T)|\mathscr F_t] = E[g(X_T)|X_t]$

Let $T > 0$. Let $(\Omega, \mathscr F, \{\mathscr F_t\}_{t \in [0,T]}, \mathbb P)$ be a filtered probability space where $\mathscr F_t = \sigma(W_u, u \in [0,t])$ where $W_t$ is standard Brownian ...
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### Solving a backwards heat equation using stochastic calculus

Given the PDE $$\frac{\partial F}{\partial t} + \frac{1}{2}\sigma^2 \frac{\partial^2 F}{\partial x^2} = 0$$ with condition $F(T,x) = x^2$, one can use the Feynman-Kac formula to arrive at F(t,x) =...
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### Regime Switching for Dynamic Correlations

I would like to implement a Regime Switching for Dynamic Correlations in an out-of-sample analysis using MATLAB. After looking at the literature on the subject, they all refer to an article by Denis ...
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### Why Markov Functional Models (Hunt 2000) are not yet so popular?

I refer to MFM introduced by Hunt [2000]. These models can be seen a subset of interest rate market models. MFM allow us to describe the term structure elements using a set a functions of a low-...
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### backward Kolmogorov equations - Markov properties

I'm a physicist who's research has lead him into the theory of stochastic differential equations. If this question is not appropriate for this forum, please feel free to delete it. So I've been ...
523 views

### Scaling of a transition matrix

I am working on a ratings transition matrix and I wondered how people scale it down to shorter time periods (although one should more or less stick to the estimation period i know). It is clear that ...
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### Pricing a piece of asset whose dividend stream following a Markovian matrix

I'm trying to calculate the result of an simple example on page 326-327, in Harrison and Kreps(1978). It's pricing a piece of asset whose dividend stream is a simple Markovian process. Here's my ...
This is an edit to the previous question, on stationary process, which was answered by Richard below. Let $x_t$ be a zero mean, time homogeneous Markovian process over time $t$ starting from $x_0=0$....