# Questions tagged [differential-equations]

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### Constant cancellation model for volume of LOB queues

I have been reading Jean-Philippe Bouchaud's book on stochastic models of LOB queues in Chapter 5, which starts with the simplest model. In this model, market/limit/cancel orders are assumed to be of ...
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1 vote
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### Step by step integration of the Hull-White SDE

I'm struggling to understand the integration process of the Hull-White equation: $$dr(t)=[\nu(t)-ar(t)]dt+\sigma dW(t)$$ In the majority of the references that I have ...
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### State space equation of CARMA(p,q) processes

Thanks for visting my question:) I am currently working on Carma(p,q) processes and do not understand how to derive the state equation. So the CARMA(p,q) process is defined by: for $p>q$ the ...
• 135
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### Ito formula and confusion with the differential operator $d$

Thanks for visiting my question. Im am currently working on this paper (https://arxiv.org/abs/2305.02523) and I am stuck at page 21 (Theorem 14 proof). First these SDE's were defined: \begin{align*} ...
• 135
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### Solving Equation for estimation risk averse parameter

Let the portfolio value follow the SDE: $$V_t=(\mu w+r(1-w))\cdot V_t\cdot dt +\sigma \cdot w\cdot V_t \cdot dB_t$$ where $\mu$ = drift of the portfolio, $\sigma$=standard deviation of the portfolio, ...
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### Dealing with the ru term in an ADI Finite Difference Scheme

I'm trying to code up the algorithm from this paper. The paper presents an ADI algorithm for pricing options in the Heston-Hull-White model. The starting point is the Heston-Hull-White PDE, given ...
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1 vote
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### Functional Analysis or Ordinary Differential Equations? [closed]

I am a current undergraduate and will be looking to apply to Quant Programs next year. This semester I have the choice between selecting Functional Analysis and Ordinary Differential Equations. I have ...
1 vote
I am trying to derive the differential of the product of two processes, but I got stuck. This is what I have until now: We have the following two stochastic processes: $dX_t= \mu_t dt +\sigma_t dW_t$...