All Questions
Tagged with stochastic-processes mathematical-finance
9 questions with no upvoted or accepted answers
3
votes
0
answers
171
views
compactness of a probability set
I have a question about the compactness of a set of martingale measures. Let $\Omega=\mathcal{C}[0,1]$ be the space of continuous functions on $[0,1]$ and $\mathcal{M}_{\Omega}$ be the family of ...
- 1,835
2
votes
0
answers
59
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How to determine speed (rate) in large deviation principle for geometric Brownian motion
By reading Asymptotics for volatility derivatives in multi-factor rough
volatility models by Lacombe, Muguruza and Stone, I am not familiar with the way they deduce the speed (or rate) when showing ...
- 21
2
votes
0
answers
261
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Asymptotics of Variable Drift Ornstein–Uhlenbeck Process
The Ornstein–Uhlenbeck process is defined as the stochastic process that solves the following SDE:
$dx_t = \theta (\mu-x_t)\,dt + \sigma\, dW_t$
where $\theta>0$, $\mu$ and $\sigma>0$ are ...
- 3,626
1
vote
0
answers
328
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Preservation of variance for log-normal variables under change of measure
Aim: to show that changing a probability measure via the application of a Radon-Nikodym derivative preserves variance of a log-normally distributed random variable (for the case when variance is non-...
- 141
1
vote
0
answers
95
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Non-diagonalizable matrix in a discretized Ornstein-Uhlenbeck process
I am attempting to implement a pairs trading algorithm for two securities by approximating a discretized version of the Ornstein-Uhlenbeck process:
\begin{equation*}
d\mathbf{S}_t = \mathbf{\kappa}(\...
- 11
1
vote
0
answers
302
views
Unique EMM & completeness in the Black-Scholes model
Consider the Black-Scholes model
$$ dS(t) = \mu(t) S(t) dt + \sigma(t) S(t) dW^{\mathbb{P}}(t) $$
$$ dB(t) = r(t) B(t) dt$$
Steele shows now in "Stochastic Calculus & Financial Applications" (Ch. ...
- 203
1
vote
0
answers
114
views
Extending risk neutral measure to insurance/mortality filtration
In insurance mathematics, one often models the underlying of an insurance policy with a Black Scholes model on a filtered probability space $(\Omega,\mathbb{Q},\mathcal{F},\mathbb{F}=(\mathcal{F}_{t}))...
- 203
1
vote
0
answers
132
views
stochastic volatility valuation equation
I'm trying to derive the valuation equation under a general stochastic volatility model. What one can read in the litterature is the following reasonning:
One consider a replicating self-financing ...
- 21
0
votes
0
answers
340
views
Why are financial markets modeled by càdlàg processes?
When opening a book or reading an article on mathematical finance, financial markets (e.g. stock prices) are always modeled by càdlàg semimartingales. I was wondering why it is that these processes ...
- 309