ABSTRACT
Rd The real Euclidian space of dimension d
Ω The set of random events P The historical probability F The σ-algebra correspond-
ing to known information (Ft)t The filtration correspond-
ing to increasing information along time t
E[X ] Expectation of the random variable X
L The set of lotteries ρ(X) Risk measure of the ran-
dom variable X RDEU Rank Dependent Expected
Utility VaR Value-at-Risk CVaR Conditional Value-at-Risk ES Expected shortfall Preference relation X i Y The random variable X s-
tochastically dominates Y at order i
Lp Space of all F -measurable random variables such that EP[Xp] is finite
E Doleans-Dade stochastic exponential
RP Return of portfolio P A′ or At Transpose of A [X,Y ] Co-variation of processesX
and Y
[X,X ] Quadratic variation of process X
〈X,X〉 Predictable compensator of process X
I The vector with all components equal to 1
IA The indicator function of the subset A
i.i.d. Independent and identically distributed
r.c.l.l Right continuous and left limited
w.r.t. With respect to CPPI Constant Proportion Port-
folio Insurance OBPI Option Based Portfolio In-
surance CARA Constant Absolute Risk
Aversion CRRA Constant Relative Risk
Aversion HARA Hyperbolic Absolute Risk
Aversion ODE Ordinary Differential Equa-
tion PDE Partial Differential Equa-
tion SDE Stochastic Differential E-
quation BSDE Backward Stochastic Dif-
ferential Equation
