We show that there exists a level of property rights completeness that leads to first-best resource exploitation; this level is different from either absent or complete property rights.
To address this question, we treat the level of completeness of property rights as a continuous variable in a renewable resource economy.
We derive an analytic expression for the optimal level of property rights completeness and discuss its policy relevance and information requirements.
The dual notions of right-completeness are easily derived from the above definition.
Unless otherwise specified, all filtrations considered in the following are supposed to satisfy the usual conditions of right continuity and completeness.
Now we define (mathcal{M}_{C mathcal{A}}) left (right) (mathcal{G} -sequentially completeness and (mathcal{M}_{C;mathcal {A}}) left (riG} -sequentially)-sequentially completeness in ((X,mandcal{mathcal{thcal{A}},ast)).
The notions of (mathcal{M}_{C mathcal{A}}) left (right) (mathcal{G} -sequential completeness and (mathcal{M}_{C;mathcal{A}}) left (riG} -sequentialW})-sequential completeness in ((X,mandcal{mathcal{thcal{A}},ast)) are defined in this section.
In this section, (mathbb {F}=left (mathcal {F}_{t}right)_{tgeq 0}) denotes a filtration satisfying the usual hypothesis of right-continuity and completeness.
Let ((Omega, mathcal {G}, mathbb {G}, mathbb {P})) be a filtered probability space satisfying the usual conditions of right-continuity and completeness, where the filtration (mathbb {G}=(mathcal {G}_{t})_{t in [0,T]}) models the flow of information available to the hedger and his counterparty.
The natural filtration of β will be denoted by (mathbb {F}^{beta }=(mathcal {F}_{t}^{beta })_{tgeq 0}): mathcal{F}_{t}^{beta}:=sigmaleft(beta_{s},0leqq sleq tright)veemathcal{N}_{P},. Note that according to (Bedini et al. 2016), Corollary 6.1, the filtration (mathbb {F}^{beta }) (denoted therein by (mathbb {F}^{P})) satisfies the usual conditions of right-continuity and completeness.
