0
votes
1answer
49 views

How to find the expectation value?

Suppose that an insurer has an exponential utility function $u(x)=−2e^{-2x}$. What is the minimum premium $P^{-}$ to be asked for a risk X? After solving this we reached the following, So,only ...
0
votes
1answer
28 views

Calculate expectation under risk neutral measure: $\mathbb{E_Q}(\max(S-1,0))$

I am busy with a numerical simulation and I want the calculate the following expectation under the risk neutral measure: $\mathbb{E_Q}(\max(S-1,0))$. $S$ is some variable that I calculated using ...
1
vote
0answers
37 views

Construct an arbitrage opportunity in a multi-period model

I am currently revising for my exam in Financial Mathematics, and I could not solve this question: For $T > 1$, consider a $T$-period model with a single risky asset and a bank account which pays ...
0
votes
0answers
32 views

Stop-Loss reinsurance, Determine the premium?

I have a question regarding the stop-loss reinsurance and the detail of this question is given as follow,
1
vote
1answer
41 views

What is the minimum Premium to be asked for a risk X?

Suppose that an insurer has an exponential utility function $u(x) =-2e^{-2x}.$ What is the minimum premium $P^{-}$ to be asked for a risk X? I got some hint for this, but I could not understand ...
1
vote
1answer
60 views

Question about the risk analysis.

In the above one can see the detail of this question, I am beginner in this kind of mathematics. I will be very greatful if any one can help me to solve them.
2
votes
1answer
88 views

Text on Probability Theory applied to Actuarial Science

I am a senior undergraduate who has passed the first three actuarial exams on probability (P), financial mathematics (FM), and models for financial economics (MFE). I am working on passing the life ...
1
vote
1answer
82 views

Stochastic differential for general semimartingale

By using the canonical representation of a semimartingale in Eberlein, Glau and Papapantoleon: "$H = B + H^c + h(x) \ast (\mu − \nu) + (x − h(x)) \ast μ$ where $h = h(x)$ is a truncation ...
0
votes
0answers
63 views

Finding arbitrage-free price interval in a relatively simple market.

Heres my problem: Define in a two time model the market as having one risky asset on $\Omega = \{\omega_1,\omega_2, \omega_3\}$, $p_i = \mathbb{P}(\{\omega_i\})>0$, and $s_i = S(\omega_i) > 0$ ...
0
votes
0answers
38 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
130 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
92 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 ...
4
votes
1answer
381 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 ...