Questions tagged [mathematical-finance]
For questions about mathematical problems arising from the study of financial markets.
71 questions
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Upsampling parameters in the Takahashi-Alexander model
Let me start by begging your forebearance; this question might at first glance appear to belong more on a forum for economics, but I hope by the end to convince you that there is mathematical content ...
- 721
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71
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Reference request: finding entries that prevent matrix from being correlation matrix
I am currently doing some research with a quantitative finance firm and my supervisor has raised an interesting question that shows up a lot with their clients: quite often, clients will want to do ...
- 721
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152
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Constrained trace optimization with relavance to optimal asset selection
Let $D$ and $Q$ be two real $m\times m$ diagonal matrices given
$$
D=\left(\begin{array}{cccc}
d_1 & 0 & \cdots & 0\\
0 & d_2 & \cdots & 0\\
\vdots & \vdots & \ddots &...
- 43
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328
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Preservation of variance for log-normal variables under change of measure
Aim: to show that changing a probability measure via the application of a Radon-Nikodym derivative preserves variance of a log-normally distributed random variable (for the case when variance is non-...
- 141
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97
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Applications of Kazamaki Conditions
I'm interested in applications of this theorem by Sekiguchi Kazamaki:
"Continuous Exponential Martingales and BMO" - Theorem 1.12:
Let $M$ be a continuous local martingale and $Z(M):= \exp(M-\frac{1}{...
- 21
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95
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Non-diagonalizable matrix in a discretized Ornstein-Uhlenbeck process
I am attempting to implement a pairs trading algorithm for two securities by approximating a discretized version of the Ornstein-Uhlenbeck process:
\begin{equation*}
d\mathbf{S}_t = \mathbf{\kappa}(\...
- 11
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68
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Recovering a Log-Correlated Gaussian Field from a limit-lognormal singular measure
In a paper I (didn't write, but) co-authored, Forecasting Volatility with the Multifractal Random Walk Model, we use explicit formulas that give the law of $(X(t),t>0)$ conditional on $(X(t),t<0)...
- 3,085
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302
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Unique EMM & completeness in the Black-Scholes model
Consider the Black-Scholes model
$$ 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
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114
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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
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82
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The Stratonovich formulation of the Double Mean Reverting Model
I am writing my Bachelor's Thesis on the fast Ninomiya-Victoir calibration of the Double Mean Reverting model and have a question to its Stratonovich formulation. I am new to mathoverflow and a novice ...
- 19
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132
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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
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1
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502
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Mathematical properties of financial prices
Prices of financial assets (stock-market prices or currency exchange rates) obviously resemble trajectories of stochastic processes.
What is known about their mathematical properties ?
I know ...
- 24.9k
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1
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151
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Construction of a probability measure from a sequence of probability measures
Summary
I would like to pass from a sequence of probability measures whose "limit" satisfies a desired property to a new probability measure that satisfies this property.
Details
We work on ...
user475819
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51
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Reconstruction of law of diffusion process from call option values
Let $X_{\cdot}$ be a $1$-dimensional diffusion process. If I know the value of the
$$\big\{\mathbb{E}[\max\{X_t,c\}\big| X_0 =x\big]:\, c\in \mathbb{R} \text{ and } \,\, t\in (0,1] \big\}.$$
Then, ...
- 5,405
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357
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Integral over a Markov process
I have the following questions:
Let $Z$ be a continuous one-dimensional Markov process on some probability space $(\Omega,\mathcal{F},\mathbb{P})$ and $\mathcal{F}_t = \sigma(Z_s,s \leq t)$. Then show ...
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Is it possible to solve $P = Cny^{-1}(1-1/(1+y/n)^{nT}) + M/(1+y/n)^{nT}$ for $y$? [closed]
The equation
$$
P = \frac{Cn}{y}\left(1-\frac{1}{(1+\frac{y}{n})^{nT}}\right)+\frac{M}{(1+\frac{y}{n})^{nT}}
$$
represents the present value (price $P$) of a government bond which pays $C$ ...
- 117
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1
answer
161
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Ratios of random variables with weak moment condition
Let $X_n$ be a sequence of iid positive random variables. Assume that $X_n$ has finite $\alpha$th moment for some value $\alpha \in (0,1)$, but infinite first moment. Assume also that the reciprocal $...
- 8,512
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1
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81
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Stochastic Geometric Progression [closed]
Let $\mu_1, \mu_2, \ldots, \mu_n, \ldots \in \mathbb{R}$, let $\sigma_1, \sigma_2,
\ldots \in [0, \infty)$ be sequences of numbers.
Let $z_1, z_2, \ldots, z_n, \ldots$ be independent random variables ...
- 13
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340
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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
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Fuzzy Logic in Finance
Has fuzzy logic been commercially applied in finance fields and has it been successful ?
I have got knowledge that it has been applied in Algorithmic trading and operational risk, but I want to know ...
- 129
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Reference request in optimal stopping [closed]
I am given the following task. Distributed over a trading day, I am supposed to buy a certain quantity of a good. The price of this good changes during the day. The goal is to buy the required ...
