📘 stochastic processes

1. **Problem statement:** We have a call center with two telephone lines. Calls arrive following a Poisson process with rate $\lambda > 0$ calls per minute. Each call duration is e

1. **Problem Statement:** We want to verify if the expression for the fourth moment of the Wiener process \(\mathbb{E}[W_{t_1}W_{t_2}W_{t_3}W_{t_4}] = t_2 t_4 + 2 t_3 t_4\) makes s

1. **Problem Statement:** We want to verify the expression for the fourth moment of a Wiener process $W_t$, specifically the expectation $\mathbb{E}[W_{t_1} W_{t_2} W_{t_3} W_{t_4}

1. Við erum að skoða ferilinn $X_t = \sigma_1 dz_1 - \sigma_2 dz_2$, þar sem $dz_1$ og $dz_2$ eru tvö Wiener-ferli með fylgni $\rho$ á milli þeirra. 2. Markmiðið er að sýna að $X_t

1. **State the problem:** We want to determine if the stochastic process $$S_t = S_0 e^{\mu t + \sigma W_t}$$ is a martingale under the risk-neutral measure, where $$W_t$$ is a sta