Tagged Questions
1
vote
0answers
24 views
Stochastic control, numerical, need expectations given coupled SDEs
I'm looking at a trio of processes which arises in a stochastic control situation. I have a process $(V_t)$ which I may control, and $(V_t)$ influences a diffusive stock price process $(S_t)$. The ...
0
votes
0answers
47 views
Drift equation / Girsanov's Theorem
Define $$\frac{dS_t}{S_t} := \mu \, dt + \sigma^B \, dB_t +\sigma^W \, dW_t,$$ $$dS_t^{(0)} := S_t^{(0)}r \, dt,$$ where the constants $\mu, \sigma^B,\sigma^W$ and $r$ all positive and $\mathcal{F}_t$ ...
0
votes
0answers
20 views
SDE(s) satisfied by Radon Nikodym derivatives of martingale measures?
Given:
Money Market Account: $dR_{t}=R_{t}r_{t}dt, R_{0}>0$
Risky Asset: $dS_{t}=S_{t}(\mu_{t}dt+\sigma_{t}dB_{t}), S_{0}>0$,
where $r, \mu,$ and $\sigma$ are positive processes and $B$ is a ...
0
votes
0answers
27 views
Non-arbitrage theory and existence of a risk premium
Consider a probability filtred space $(\Omega, \mathcal F, \mathbb F, \mathbb P)$, where $\mathbb F = (\mathcal F_t)_{0\leq t\leq T}$ satisfing the habitual conditions and isgenerated by $1 d $- ...
2
votes
1answer
118 views
Is the following a martingale?
Let $X_{n}$ be a martingale with respect to a filtration $\mathbb{P}_{n}$. Define:
$Y_{n}$ := $X_{n}^{3}$
Is $Y_{n}$ a martingale? Supermartingale?
0
votes
0answers
68 views
Black Scholes PDE for non-constant coefficients
I need to derive the Black–Scholes PDE for non-constant coefficients. I suppose we should also use an appropriate transformation such as $y=\ln S$. I have no idea, please help me.
3
votes
1answer
87 views
Black scholes model type
I want to study the following market:
$$S_1(t)=S_1(t)(\mu_1dt + \sigma_1dW_1(t))$$
$$S_2(t)=S_2(t)(\mu_2dt+\sigma_2dW_2(t))$$
for $t\in [0,T]$, constants $\mu_i,\sigma_i$, initial values ...
1
vote
0answers
65 views
Compactness of the set of densities of equivalent martingale measures
Consider an incomplete market $(\Omega,\mathcal F,\mathbb P)$ driven by a semimartingale $S=(S_t)_{t\in[0,T]}$. Under the no free lunch under vanishing risk (NFLVR) assumption, the set $\mathcal ...
3
votes
1answer
165 views
Futures pricing and futures price process under the real world measure
This is something that keeps bothering me about the Benchmark approach of Platen, which (very) shortly is as follows: Compare the development of an economic value with a growth optimal portfolio. ...
3
votes
1answer
241 views
Applications of Compound Poisson Processes
I'm reading the book Non-Life Insurance Mathematics, an introduction with Stochastic Processes by Thomas Mikosch and I'm interested in applications of the Cramer-Lundberg Process to concrete examples ...
2
votes
1answer
325 views
What is the definition of a “predictable process”?
I am reading a book on financial mathematics, and frequently encounter the phrase "predictable process", which I haven't seen definition of, and cannot find the definition online.
At first I thought ...
2
votes
2answers
318 views
Using Black-Scholes Equation to “buy” stocks
From what I understand, Black-Scholes equation in finance is used to price options which are a contract between a potential buyer and a seller. Can I use this mathematical framework to "buy" a stock? ...
4
votes
5answers
3k views
Understanding Black-Scholes
Assume I have only basic math knowledge, what specific areas of math would I need to learn in order to understand the following webpage:
Black-Scholes
Many thanks.
