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论文研究-基于限价订单簿的最优高频做市商策略研究.pdf
38 1
2018 1
Systems Engineering — Theory & Practice
Vol.38, No.1
Jan., 2018
doi: 10.12011/1000-6788(2018)01-0016-19
: F830
: A
1, 2, 1
(1. , 100081; 2. , 100081)
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Optimal high-frequency market making strategy research based
on limit order book
SONG Bin1, LIN Mu2, TIAN Yijia1
(1. Investment Department, School of Management Science and Engineering, Central University of Finance and Economics,
Beijing 100081, China; 2. Applied Mathematics Department, School of Statistics and Mathematics, Central University of
Finance and Economics, Beijing 100081, China)
Abstract Based on considering the execution and inventory risk, the spread process is modelled and the
inventory penalty function is also introduced. The market-making strategy is to maximize the expected
utility function. The solution of the strategy can be considered as a stochastic optimal control problem.
Employing the dynamic programming principle, the stochastic optimal control problem can be written as
related variational inequality and solved by finite difference method. The order submissions given by the
strategy are in accord with the assumption for execution density, spread and inventory’ effect on order
submission. The empirical and reliable tests of the strategy show that it has stable profitability under
reasonable assumptions.
Keywords market-making strategy; limit-order-book; stochastic control; finite difference
1
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35%. , 80%[1]. , ,
. Menkveld[1], Hendershott, Jones Menkveld[2]
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: 2016-08-08
: (51609270); (14YJA790048)
Foundation item: National Natural Science Foundation of China (51609270); Ministry of Education Humanities and Social
Sciences Research and Planning Fund (14YJA790048)
: (1971–), , , , , , : , E-mail:
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mail: mlin@cufe.edu.cn; Æ (1991–), , , !, %, : !, E-mail:
863786929@qq.com.
: , , Æ. " [J]. ##’ $, 2018, 38(1): 16–34.
: Song B, Lin M, Tian Y J. Optimal high-frequency market making strategy research based on limit order book[J].
Systems Engineering — Theory & Practice, 2018, 38(1): 16–34.
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λb
i(qb)
)lb × ϕi(t, y + lb) − ϕi(t, y)
2 −δ1
−η( iδ
qb=Bb+
j=1
e
rij(t)[ϕj(t, y) − ϕi(t, y)]
−
−
bny − 1
max
− ∂ϕi
∂t
+
inf
(qb,lb)∈Qb
i×[0,¯l]
inf
i ×[0,¯l]
(qa,la)∈Qa
ϕi(t, y) − inf
e∈[−¯e,¯e]
λa
i (qa)[e
eη|e| iδ
23
(25)
(26)
(27)
(28)
(29)
(30)
(31)
(32)
(33)
−η( iδ
2 −δ1qa =Ba+ )la × ϕi(t, y − la) − ϕi(t, y)] + γg(y),
2 ϕi(t, y + e)
= 0
CgDC:
ϕi(T, y) = eη|y| iδ
2
(ϕh
i )i∈Im K9& >K:
˜ϕi(tk, y) =
1
4
+
+
(bny − 1
inf
(qb,lb)∈Qb
inf
(qa,la)∈Qa
i ×[0,¯l]
2
i (tn, y) = eη|y| iδ
ϕh
2 σ2(ηy)2 + μ(1 − κηy − e−ηκy))ϕh
4h × ϕi
4h × ϕi
2 −δ1qa=Ba− )laN i,qa
)lbN i,qb
2 −δ1
−η( iδ
−η( iδ
qb=Bb+
E
E
e
e
i×[0,¯l]
i (tk+1, y) + E
tk+1, y, S
tk,iδ
tk+4
ϕh
tk+1, y + lb N
tk+1, y − la N
i,qb
4h
i,qa
4h
− hγg(y)
eη|e| iδ
2 × ϕh
i (tk+1, y + e)
, k = 0,··· , n − 1
φi(tk, y) = min
˜ϕi(tk, y),
inf
e∈[−¯e,,¯e]
4 MBNM PP
4.1 QIR
.<" Y Z K, 6I A AAF
d (000004.SZ) 2015 e 2 a 3 5Z$(5Z K;.
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