Optimal Consumption And Portfolio Choice With Borrowing Constraints
Optimal Consumption And Portfolio Choice With Borrowing Constraints
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3) is uniformly elliptic and see Krylov (1987). ■ The next lemma says that the above sequence J' converges to J, as « goes to zero.
Lemma 3. 3: J' converges to J locally uniformly as e goes to 0.
Proof: See appendix B. ■ We next prove that the first and second derivatives of J* are bounded away from zero uniformly in e. This implies in particular that the optimal X in equation (3. 3) is bounded away from zero.
Lemma 3. 4: In any interval [a, b], there exists two positive constants R, =R, ([a, b...]) and R2=R2([a, bJ) independent of (. , such that, for lVe[a, b], (i) J"(W)>R, (3. 4) (ii) \J'"{W} \-tJLXV (W)} + max {u{c)-cV (^W)} -^rWyi^W) WG[a, b iifli - 2 ciO aR2 V{a)=J'(a), V{b)=J*{b) .
(3. 6) 14 Applying classical results from the theory of elliptic differential equations (see, for example, Krylov (1987)), we get that (3. 6) has a smooth solution V which by uniqueness and lemma 3.
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You can find similar books in the "Read Also" column, or choose other free books by Jean Luc Vila to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
3) is uniformly elliptic and see Krylov (1987). ■ The next lemma says that the above sequence J' converges to J, as « goes to zero.
Lemma 3. 3: J' converges to J locally uniformly as e goes to 0.
Proof: See appendix B. ■ We next prove that the first and second derivatives of J* are bounded away from zero uniformly in e. This implies in particular that the optimal X in equation (3. 3) is bounded away from zero.
Lemma 3. 4: In any interval [a, b], there exists two positive constants R, =R, ([a, b...]) and R2=R2([a, bJ) independent of (. , such that, for lVe[a, b], (i) J"(W)>R, (3. 4) (ii) \J'"{W} \
(3. 6) 14 Applying classical results from the theory of elliptic differential equations (see, for example, Krylov (1987)), we get that (3. 6) has a smooth solution V which by uniqueness and lemma 3.
What to read after Optimal Consumption And Portfolio Choice With Borrowing Constraints?
You can find similar books in the "Read Also" column, or choose other free books by Jean Luc Vila to read onlineMoreLess
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