What are the optimal investment strategies for dynamically reallocating assets with different risks?
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Let's consider the following simplified model.
Suppose you start with some money and invest for a fixed amount of time T. You have one risky asset and one risk free asset to choose from. The risky asset follows a geometric Brownian motion with drift mu and volatility sigma. The risk free asset has rate r, continuously compounded. (continued)
stochastic-processes finance control-theory
asked Dec 14 '18 at 19:28
user3320467user3320467
11
$endgroup$
add a comment |
$begingroup$
Let's consider the following simplified model.
Suppose you start with some money and invest for a fixed amount of time T. You have one risky asset and one risk free asset to choose from. The risky asset follows a geometric Brownian motion with drift mu and volatility sigma. The risk free asset has rate r, continuously compounded. (continued)
stochastic-processes finance control-theory
asked Dec 14 '18 at 19:28
user3320467user3320467
11
$endgroup$
$begingroup$
As usual 0<r<mu. You can change the ratio of the two assets any time throughout your investment period, and you can also short/borrow the two assets. You want the best risk-return tradeoff at the end. What strategies are located at the frontier of the risk-return, ie E(R) vs Std(R), plot? What does the frontier look like? We know from the Black Scholes model that options are equivalent to some dynamical reallocation strategy, but do options stay at the frontier of the risk-return curve?
$endgroup$
– user3320467
Dec 15 '18 at 23:30
add a comment |
$begingroup$
Let's consider the following simplified model.
Suppose you start with some money and invest for a fixed amount of time T. You have one risky asset and one risk free asset to choose from. The risky asset follows a geometric Brownian motion with drift mu and volatility sigma. The risk free asset has rate r, continuously compounded. (continued)
stochastic-processes finance control-theory
asked Dec 14 '18 at 19:28
user3320467user3320467
11
$endgroup$
Let's consider the following simplified model.
Suppose you start with some money and invest for a fixed amount of time T. You have one risky asset and one risk free asset to choose from. The risky asset follows a geometric Brownian motion with drift mu and volatility sigma. The risk free asset has rate r, continuously compounded. (continued)
stochastic-processes finance control-theory
stochastic-processes finance control-theory
asked Dec 14 '18 at 19:28
user3320467user3320467
11
asked Dec 14 '18 at 19:28
user3320467user3320467
11
edited Dec 15 '18 at 23:27
user3320467
asked Dec 14 '18 at 19:28
user3320467user3320467
11
asked Dec 14 '18 at 19:28
user3320467user3320467
11
asked Dec 14 '18 at 19:28
user3320467user3320467
11
11
$begingroup$
As usual 0<r<mu. You can change the ratio of the two assets any time throughout your investment period, and you can also short/borrow the two assets. You want the best risk-return tradeoff at the end. What strategies are located at the frontier of the risk-return, ie E(R) vs Std(R), plot? What does the frontier look like? We know from the Black Scholes model that options are equivalent to some dynamical reallocation strategy, but do options stay at the frontier of the risk-return curve?
$endgroup$
– user3320467
Dec 15 '18 at 23:30
add a comment |
$begingroup$
As usual 0<r<mu. You can change the ratio of the two assets any time throughout your investment period, and you can also short/borrow the two assets. You want the best risk-return tradeoff at the end. What strategies are located at the frontier of the risk-return, ie E(R) vs Std(R), plot? What does the frontier look like? We know from the Black Scholes model that options are equivalent to some dynamical reallocation strategy, but do options stay at the frontier of the risk-return curve?
$endgroup$
– user3320467
Dec 15 '18 at 23:30
$begingroup$
As usual 0<r<mu. You can change the ratio of the two assets any time throughout your investment period, and you can also short/borrow the two assets. You want the best risk-return tradeoff at the end. What strategies are located at the frontier of the risk-return, ie E(R) vs Std(R), plot? What does the frontier look like? We know from the Black Scholes model that options are equivalent to some dynamical reallocation strategy, but do options stay at the frontier of the risk-return curve?
$endgroup$
– user3320467
Dec 15 '18 at 23:30
$begingroup$
As usual 0<r<mu. You can change the ratio of the two assets any time throughout your investment period, and you can also short/borrow the two assets. You want the best risk-return tradeoff at the end. What strategies are located at the frontier of the risk-return, ie E(R) vs Std(R), plot? What does the frontier look like? We know from the Black Scholes model that options are equivalent to some dynamical reallocation strategy, but do options stay at the frontier of the risk-return curve?
$endgroup$
– user3320467
Dec 15 '18 at 23:30
add a comment |
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$begingroup$
As usual 0<r<mu. You can change the ratio of the two assets any time throughout your investment period, and you can also short/borrow the two assets. You want the best risk-return tradeoff at the end. What strategies are located at the frontier of the risk-return, ie E(R) vs Std(R), plot? What does the frontier look like? We know from the Black Scholes model that options are equivalent to some dynamical reallocation strategy, but do options stay at the frontier of the risk-return curve?
$endgroup$
– user3320467
Dec 15 '18 at 23:30