The first of the parallels relates to the desolating sacrilege.
The erection of the statue of Jupiter can be understood as an impending abomination:
31 Forces sent by him shall occupy and profane the temple and fortress. They shall abolish the regular burnt offering and set up the abomination that makes desolate. 32 He shall seduce with intrigue those who violate the covenant; but the people who are loyal to their God shall stand firm and take action. 33 The wise among the people shall give understanding to many;
Daniel 12:
10 None of the wicked shall understand, but those who are wise shall understand. 11 From the time that the regular burnt offering is taken away and the abomination that desolates is set up, there shall be one thousand two hundred ninety days. 12 Happy are those who persevere and attain the thousand three hundred thirty-five days. 13 But you, go your way, and rest; you shall rise for your reward at the end of the days.
This connection is made in Mark:
12 Brother will betray brother to death, and a father his child, and children will rise against parents and have them put to death; 13 and you will be hated by all because of my name. But the one who endures to the end will be saved.
14 “But when you see the desolating sacrilege set up where it ought not to be (let the reader understand), then those in Judea must flee to the mountains; 15 the one on the housetop must not go down or enter the house to take anything away; 16 the one in the field must not turn back to get a coat. 17 Woe to those who are pregnant and to those who are nursing infants in those days! 18 Pray that it may not be in winter. 19 For in those days there will be suffering, such as has not been from the beginning of the creation that God created until now, no, and never will be.
Of course the erection of the statue of Jupiter by Caligula never happened. The statue was never erected and nothing came of the incident.
But the next parallel is between the mocking of Jesus and the mocking of a Jewish invalid in Against Flaccus.
This account shares a number of striking similarities with the mocking of Jesus in the Gospel of Mark.
15 So Pilate, wishing to satisfy the crowd, released Barabbas for them; and after flogging Jesus, he handed him over to be crucified.
16 Then the soldiers led him into the courtyard of the palace (that is, the governor’s headquarters); and they called together the whole cohort. 17 And they clothed him in a purple cloak; and after twisting some thorns into a crown, they put it on him. 18 And they began saluting him, “Hail, King of the Jews!” 19 They struck his head with a reed, spat upon him, and knelt down in homage to him. 20 After mocking him, they stripped him of the purple cloak and put his own clothes on him. Then they led him out to crucify him.
Finally, in On the Embassy to Gaius, Philo portrays Pilate as a cruel ruler hostile to the Jews, who presided over unjust executions.
he feared least they might in reality go on an embassy to the emperor, and might impeach him with respect to other particulars of his government, in respect of his corruption, and his acts of insolence, and his rapine, and his habit of insulting people, and his cruelty, and his continual murders of people untried and uncondemned, and his never ending, and gratuitous, and most grievous inhumanity.
...
And he, when he had read it, what did he say of Pilate, and what threats did he utter against him! But it is beside our purpose at present to relate to you how very angry he was, although he was not very liable to sudden anger; since the facts speak for themselves; for immediately, without putting any thing off till the next day, he wrote a letter, reproaching and reviling him in the most bitter manner for his act of unprecedented audacity and wickedness, and commanding him immediately to take down the shields and to convey them away from the metropolis of Judaea to Caesarea, on the sea which had been named Caesarea Augusta, after his grandfather, in order that they might be set up in the temple of Augustus. And accordingly, they were set up in that edifice. And in this way he provided for two matters: both for the honor due to the emperor, and for the preservation of the ancient customs of the city.
"Now the things set up on that occasion were shields, on which there was no representation of any living thing whatever engraved. But now the thing proposed to be erected is a colossal statue.
So, Philo presented Pilate as the governor of Judea who presided over a wicked offense that foreshadowed the erection of a “desolating sacrilege” in the Temple.
So in these works of Philo we have an account of a Jewish invalid who is mocked as a "king of the Jews", the description of a “desolating sacrilege” that is destined to be placed in the Temple, leading to the downfall of the Jewish nation, and Pilate is described as the Roman governor whose actions foreshadowed the future corruption of the Temple and the demise of the Jewish people.
Now, conservative scholars have long recognized much of this, and argued that Philo's work corroborates the "prediction" of Jesus. Their argument is that the real Jesus must have been foretelling the events of the Caligula Crisis. So one argument is that the real Jesus had knowledge of the Caligula Crisis or that there was rumblings of it, etc.
But the problem is that the Caligula Crisis didn't arise until AFTER Pilate was out of office. One can assume a "divine" knowledge, but then the crisis never actually happened, so...
If we just set trying to explain anything aside, it seems to me that the case is quite strong that Mark 13-15 is dependent upon the writings of Philo. Again, set the question of "why" aside for now and just address the literary relationships.
Is the ending of the Gospel of Mark sourced from Philo?