Optimal Investment and Consumption with Liquid and Illiquid Assets

Choi, Jin Hyuk

doi:10.2139/ssrn.3159673

Cited by 5 publications

(14 citation statements)

References 27 publications

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“…Nonetheless, the methods of this paper can be generalized to the multiasset case, albeit only to a special case in which transaction costs are payable on one asset only. See Hobson, Tse, and Zhu () and Choi ().…”

Section: Conclusion and Further Remarksmentioning

confidence: 99%

Optimal consumption and investment under transaction costs*

Hobson

Tse

Zhu

2018

Mathematical Finance

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In this paper, we consider the Merton problem in a market with a single risky asset and proportional transaction costs. We give a complete solution of the problem up to the solution of a first-crossing problem for a first-order differential equation. We find that the characteristics of the solution (e.g., well-posedness) can be related to some simple properties of a univariate quadratic whose coefficients are functions of the parameters of the problem. Our solution to the problem via the value function includes expressions for the boundaries of the no-transaction wedge. Using these expressions, we prove a precise condition for when leverage occurs. One new and unexpected result is that when the solution to the Merton problem (without transaction costs) involves a leveraged position, and when transaction costs are large, the location of the boundary at which sales of the risky asset occur is independent of the transaction cost on purchases. K E Y W O R D SMerton problem, proportional transaction costs, no transaction region, well-posedness, leverage Mathematical Finance. 2019;29:483-506.wileyonlinelibrary.com/journal/mafi

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Section: Conclusion and Further Remarksmentioning

confidence: 99%

Optimal consumption and investment under transaction costs*

Hobson

Tse

Zhu

2018

Mathematical Finance

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“…The works most closely related to ours are the papers by Dai et al (2011), Bichuch and Guasoni (2003) and Choi (2018), who all studied the optimal investment problem with a risk-free asset and two risky assets, a liquid and an illiquid one. All these papers derive the no-trade region explicitly under very general conditions.…”

Section: Literature Reviewmentioning

confidence: 88%

Hedge or Rebalance: Optimal Risk Management with Transaction Costs

Gallien¹,

Kassibrakis²,

Malamud

2018

Risks

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We solve the problem of optimal risk management for an investor holding an illiquid, alpha-generating fund and hedging his/her position with a liquid futures contract. When the investor is subject to a lower bound on net return, he/she is forced to reduce the total risk of his/her portfolio after a loss. In this case, he/she faces a tradeoff of either paying the transaction costs and deleveraging or keeping his/her current position in the illiquid instrument and hedging away some of the risk while keeping the residual, unhedgeable risk on his/her balance sheet. We explicitly characterize this tradeoff and study its dependence on asset characteristics. In particular, we show that higher alpha and lower beta typically widen the no-trading zone, while the impact of volatility is ambiguous.

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“…This set-up has been extended to general complete market models through the works of Pliska (1986), Karatzas et al (1987) and Cox and Huang (1989). Further extensions were achieved trough the addition of transaction costs in Davis and Norman (1990), Shreve and Soner (1994), Cuoco and Liu (2000) and Kallsen and Muhle-Karbe (2010), illiquid assets in Desmettre and Seifried (2016), Choi (2020) as well as stochastic volatility in Liu and Pan (2003), Kraft (2005) and Branger et al (2008). Moreover, general optimality results for incomplete markets were derived in Karatzas et al (1991), Kramkov and Schachermayer (1999) and Larsen and Žitkoviç (2013).…”

Section: Introductionmentioning

confidence: 99%

Portfolio optimization: not necessarily concave utility and constraints on wealth and allocation

2022

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We consider a portfolio optimization problem for a utility maximizing investor who is simultaneously restricted by convex constraints on portfolio allocation and upper and lower bounds on terminal wealth. After introducing a capped version of the Legendre–Fenchel-transformation, we use it to suitably extend the well-known auxiliary market framework for convex allocation constraints to derive equivalent optimality conditions for our setting with additional bounds on terminal wealth. The considered utility does not have to be strictly concave or smooth, as long as it can be concavified.

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Optimal Investment and Consumption with Liquid and Illiquid Assets

Cited by 5 publications

References 27 publications

Optimal consumption and investment under transaction costs*

Optimal consumption and investment under transaction costs*

Hedge or Rebalance: Optimal Risk Management with Transaction Costs

Portfolio optimization: not necessarily concave utility and constraints on wealth and allocation

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