How do investors' expectations drive asset prices?

u(t,x₁,x₂ )

Xi exp ^-x₂ J^ λ¹ ∖s)ds)

exp ɑʃ (—λ^²∖r) σ^y (r) + b(r)^ ^ʃ — ʌɑ∖s)ds) dr)

Hence, F_t is given by

F_t = I_t exp -~^σt ʃ ʌɑ∖s)ds^

exp

exp

^- ʃ (—λ^²∙∖r) σ'^ (r) + b(rɔ ^ʃ ʌɑ∖s)ds) dr)
( f ^T1 σ (r))²f f    ∖s>y dr} , 0 ≤ t ≤ T,

and

^Z' = (⅞> )= ^F ' —'σ'(t)ʃ, <∙ >(^)d_s )

The forward price of the asset can be rewritten as

dF = F_tσf (√1 — p_t²λ<¹ ∖t) + У²∖t)p_i)dt

+F_tσξ (√1 — p_t²dW_t¹ + p_t dW_t,  0 ≤ t ≤ T,

(14)

with

F_iσf := ∖∕(Z<¹ >)² + (Z,<² <

and

F
.
₁∕(z_l<'> )²+ (zy)²

(15)

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