# Tag Info

Accepted

### Is first order stochastic dominance conserved under change of measure?

Consider a coin independently tossed 10 times. Assume under the measure $P$, $Pr(H)$ > 0.5 but not equal to 1. Let a risk neutral person be iteratively given the gamble between getting atleast $n$ ...
• 1,905
Accepted

### Change of measure for a stochastic process to be a martingale

Let $Y_t= e^{B_t}$ and $Z_t = B_{t}-t / 2$. Then, \begin{align*} dX_t &= Z_t dY_t + Y_t dZ_t + d\langle Y, Z\rangle_t\\ &=(B_{t}-t / 2)e^{B_t}\big( dB_t + 1/2\,dt \big) + e^{B_t}\big(dB_t -1/2\...
• 21.1k

### Change of measure for a stochastic process to be a martingale

(Now that I saw Gordon's solution, I can finish my attempt; I had noticed $dB_t +1/2dt$ immediately from product rule for $V_t$, zero quadratic covariation between $t/2$ and $e^{B_t}$, but hours later ...
• 5,043
1 vote

### Equivalent local martingale measure vs. equvalent martingale measure in a Brownian setup

The examples provided by Sin in their article Complications with Stochastic Volatility Models might help to answer your questions. I'm transcribing the abstract below: We show a class of stochastic ...
• 5,043
1 vote

$N_t$ process comes with its own Poisson law (probability measure) $P$ defined via intensity $\lambda$. Under it, $N_t-\lambda t$ is a martingale wrt ${\cal F}_t =\sigma(N_u | u\in [0,t])$ (as $E^P[... • 5,043 1 vote ### Poisson process under equivalent martingale measure Consider a radon nikodym derivative, the Random variable:$Z(w)= 1_{N(T,w)=1}+1-Pr(N(T)=1)$. It is admissible since it is always positive and has an expectation 1. This will lead us to the formation ... • 1,905 1 vote Accepted ### EMM for Bachelier model It sounds to me like you understand everything apart from how Girsanov's theorem defines the EMM. Girsanov's theorem tells us that if$B_t$is standard Brownian motion under$P$, then for any adapted ... • 466 1 vote Accepted ### How to prove that the following is still a Brownian motion I try to clarify. First, let us be under the real world probability measure$\mathbb{P}$. Say that the process$Y_t$is a$\mathbb{P}$standard Brownian motion. Then the following is true by ... 1 vote ### We have a two LIBOR contracts, how to compare their values by change of change of numeraire Let$X_{T_1}$be a random quantity known (fixed) at$T_1$(measurable wrt$T_1$-information),$B$be the standard bank account and$P$standard zero-coupon bond price. From standard pricing, for the ... • 5,043 1 vote Accepted ### Market Price of Risk for Consumption Asset - Hull's Example 28.1 Note that just before Equation (28.9), Hull writes$-$my emphasis: The market price of risk of [asset]$\theta\$ measures the trade-offs between risk and return that are made for securities ...
• 8,059

Only top scored, non community-wiki answers of a minimum length are eligible